Partial Differential Equations And Applications

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Introduction to Partial Differential Equations with Applications

Introduction to Partial Differential Equations with Applications
  • Author : E. C. Zachmanoglou,Dale W. Thoe
  • Publisher : Courier Corporation
  • Release Date : 2012-04-20
  • Total pages : 432
  • ISBN : 9780486132174
  • File Size : 51,8 Mb
  • Total Download : 696
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This text explores the essentials of partial differential equations as applied to engineering and the physical sciences. Discusses ordinary differential equations, integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory, more. Problems and answers.

Nonlinear Partial Differential Equations with Applications

Nonlinear Partial Differential Equations with Applications
  • Author : Tomás Roubicek
  • Publisher : Springer Science & Business Media
  • Release Date : 2006-01-17
  • Total pages : 405
  • ISBN : 9783764373979
  • File Size : 17,5 Mb
  • Total Download : 297
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This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition quickly leads general theory to analysis of concrete equations, which have specific applications in such areas as electrically (semi-) conductive media, modeling of biological systems, and mechanical engineering. Methods of Galerkin or of Rothe are exposed in a large generality.

Solving Partial Differential Equation Applications with PDE2D

Solving Partial Differential Equation Applications with PDE2D
  • Author : Granville Sewell
  • Publisher : John Wiley & Sons
  • Release Date : 2018-10-09
  • Total pages : 224
  • ISBN : 9781119507932
  • File Size : 47,6 Mb
  • Total Download : 546
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Solve engineering and scientific partial differential equation applications using the PDE2D software developed by the author Solving Partial Differential Equation Applications with PDE2D derives and solves a range of ordinary and partial differential equation (PDE) applications. This book describes an easy-to-use, general purpose, and time-tested PDE solver developed by the author that can be applied to a wide variety of science and engineering problems. The equations studied include many time-dependent, steady-state and eigenvalue applications such as diffusion, heat conduction and convection, image processing, math finance, fluid flow, and elasticity and quantum mechanics, in one, two, and three space dimensions. The author begins with some simple "0D" problems that give the reader an opportunity to become familiar with PDE2D before proceeding to more difficult problems. The book ends with the solution of a very difficult nonlinear problem, which requires a moving adaptive grid because the solution has sharp, moving peaks. This important book: Describes a finite-element program, PDE2D, developed by the author over the course of 40 years Derives the ordinary and partial differential equations, with appropriate initial and boundary conditions, for a wide variety of applications Offers free access to the Windows version of the PDE2D software through the author’s website at www.pde2d.com Offers free access to the Linux and MacOSX versions of the PDE2D software also, for instructors who adopt the book for their course and contact the author at www.pde2d.com Written for graduate applied mathematics or computational science classes, Solving Partial Differential Equation Applications with PDE2D offers students the opportunity to actually solve interesting engineering and scientific applications using the accessible PDE2D.

partial differential equations and applications

partial differential equations and applications
  • Author : Giorgio Talenti,Edoardo Vesentini,Paolo Marcellini
  • Publisher : CRC Press
  • Release Date : 1996-01-16
  • Total pages : 392
  • ISBN : 0824796985
  • File Size : 41,6 Mb
  • Total Download : 476
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Written as a tribute to the mathematician Carlo Pucci on the occasion of his 70th birthday, this is a collection of authoritative contributions from over 45 internationally acclaimed experts in the field of partial differential equations. Papers discuss a variety of topics such as problems where a partial differential equation is coupled with unfavourable boundary or initial conditions, and boundary value problems for partial differential equations of elliptic type.

Introduction to Partial Differential Equations with Applications

Introduction to Partial Differential Equations with Applications
  • Author : E. C. Zachmanoglou,Dale W. Thoe
  • Publisher : Courier Corporation
  • Release Date : 1986-01-01
  • Total pages : 434
  • ISBN : 9780486652511
  • File Size : 9,6 Mb
  • Total Download : 854
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Download Introduction to Partial Differential Equations with Applications in PDF, Epub, and Kindle

This text explores the essentials of partial differential equations as applied to engineering and the physical sciences. Discusses ordinary differential equations, integral curves and surfaces of vector fields, the Cauchy-Kovalevsky theory, more. Problems and answers.

Stochastic Partial Differential Equations and Applications

Stochastic Partial Differential Equations and Applications
  • Author : Giuseppe Da Prato,Luciano Tubaro
  • Publisher : CRC Press
  • Release Date : 2002-04-05
  • Total pages : 480
  • ISBN : 0203910176
  • File Size : 34,9 Mb
  • Total Download : 200
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Download Stochastic Partial Differential Equations and Applications in PDF, Epub, and Kindle

Based on the proceedings of the International Conference on Stochastic Partial Differential Equations and Applications-V held in Trento, Italy, this illuminating reference presents applications in filtering theory, stochastic quantization, quantum probability, and mathematical finance and identifies paths for future research in the field. Stochastic Partial Differential Equations and Applications analyzes recent developments in the study of quantum random fields, control theory, white noise, and fluid dynamics. It presents precise conditions for nontrivial and well-defined scattering, new Gaussian noise terms, models depicting the asymptotic behavior of evolution equations, and solutions to filtering dilemmas in signal processing. With contributions from more than 40 leading experts in the field, Stochastic Partial Differential Equations and Applications is an excellent resource for pure and applied mathematicians; numerical analysts; mathematical physicists; geometers; economists; probabilists; computer scientists; control, electrical, and electronics engineers; and upper-level undergraduate and graduate students in these disciplines.

Applications of Lie's Theory of Ordinary and Partial Differential Equations

Applications of Lie's Theory of Ordinary and Partial Differential Equations
  • Author : L Dresner
  • Publisher : CRC Press
  • Release Date : 1998-01-01
  • Total pages : 242
  • ISBN : 1420050788
  • File Size : 10,9 Mb
  • Total Download : 741
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Lie's group theory of differential equations unifies the many ad hoc methods known for solving differential equations and provides powerful new ways to find solutions. The theory has applications to both ordinary and partial differential equations and is not restricted to linear equations. Applications of Lie's Theory of Ordinary and Partial Differential Equations provides a concise, simple introduction to the application of Lie's theory to the solution of differential equations. The author emphasizes clarity and immediacy of understanding rather than encyclopedic completeness, rigor, and generality. This enables readers to quickly grasp the essentials and start applying the methods to find solutions. The book includes worked examples and problems from a wide range of scientific and engineering fields.

Theory and Applications of Partial Functional Differential Equations

Theory and Applications of Partial Functional Differential Equations
  • Author : Jianhong Wu
  • Publisher : Springer Science & Business Media
  • Release Date : 2012-12-06
  • Total pages : 432
  • ISBN : 9781461240501
  • File Size : 54,7 Mb
  • Total Download : 775
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Abstract semilinear functional differential equations arise from many biological, chemical, and physical systems which are characterized by both spatial and temporal variables and exhibit various spatio-temporal patterns. The aim of this book is to provide an introduction of the qualitative theory and applications of these equations from the dynamical systems point of view. The required prerequisites for that book are at a level of a graduate student. The style of presentation will be appealing to people trained and interested in qualitative theory of ordinary and functional differential equations.

Partial Differential Equations

Partial Differential Equations
  • Author : Victor Henner,Tatyana Belozerova,Alexander Nepomnyashchy
  • Publisher : CRC Press
  • Release Date : 2019-11-20
  • Total pages : 298
  • ISBN : 9780429804410
  • File Size : 39,8 Mb
  • Total Download : 738
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Partial Differential Equations: Analytical Methods and Applications covers all the basic topics of a Partial Differential Equations (PDE) course for undergraduate students or a beginners’ course for graduate students. It provides qualitative physical explanation of mathematical results while maintaining the expected level of it rigor. This text introduces and promotes practice of necessary problem-solving skills. The presentation is concise and friendly to the reader. The "teaching-by-examples" approach provides numerous carefully chosen examples that guide step-by-step learning of concepts and techniques. Fourier series, Sturm-Liouville problem, Fourier transform, and Laplace transform are included. The book’s level of presentation and structure is well suited for use in engineering, physics and applied mathematics courses. Highlights: Offers a complete first course on PDEs The text’s flexible structure promotes varied syllabi for courses Written with a teach-by-example approach which offers numerous examples and applications Includes additional topics such as the Sturm-Liouville problem, Fourier and Laplace transforms, and special functions The text’s graphical material makes excellent use of modern software packages Features numerous examples and applications which are suitable for readers studying the subject remotely or independently

Theory and Applications of Partial Differential Equations

Theory and Applications of Partial Differential Equations
  • Author : Piero Bassanini,Alan R. Elcrat
  • Publisher : Unknown
  • Release Date : 2014-01-15
  • Total pages : 456
  • ISBN : 1489918760
  • File Size : 32,5 Mb
  • Total Download : 522
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PDF book entitled Theory and Applications of Partial Differential Equations written by Piero Bassanini,Alan R. Elcrat and published by Unknown which was released on 2014-01-15 with total hardcover pages 456, the book become popular and critical acclaim.

Differential Equation Analysis in Biomedical Science and Engineering

Differential Equation Analysis in Biomedical Science and Engineering
  • Author : William E. Schiesser
  • Publisher : John Wiley & Sons
  • Release Date : 2014-03-31
  • Total pages : 344
  • ISBN : 9781118705162
  • File Size : 45,6 Mb
  • Total Download : 684
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Features a solid foundation of mathematical and computational tools to formulate and solve real-world PDE problems across various fields With a step-by-step approach to solving partial differential equations (PDEs), Differential Equation Analysis in Biomedical Science and Engineering: Partial Differential Equation Applications with R successfully applies computational techniques for solving real-world PDE problems that are found in a variety of fields, including chemistry, physics, biology, and physiology. The book provides readers with the necessary knowledge to reproduce and extend the computed numerical solutions and is a valuable resource for dealing with a broad class of linear and nonlinear partial differential equations. The author’s primary focus is on models expressed as systems of PDEs, which generally result from including spatial effects so that the PDE dependent variables are functions of both space and time, unlike ordinary differential equation (ODE) systems that pertain to time only. As such, the book emphasizes details of the numerical algorithms and how the solutions were computed. Featuring computer-based mathematical models for solving real-world problems in the biological and biomedical sciences and engineering, the book also includes: R routines to facilitate the immediate use of computation for solving differential equation problems without having to first learn the basic concepts of numerical analysis and programming for PDEs Models as systems of PDEs and associated initial and boundary conditions with explanations of the associated chemistry, physics, biology, and physiology Numerical solutions of the presented model equations with a discussion of the important features of the solutions Aspects of general PDE computation through various biomedical science and engineering applications Differential Equation Analysis in Biomedical Science and Engineering: Partial Differential Equation Applications with R is an excellent reference for researchers, scientists, clinicians, medical researchers, engineers, statisticians, epidemiologists, and pharmacokineticists who are interested in both clinical applications and interpretation of experimental data with mathematical models in order to efficiently solve the associated differential equations. The book is also useful as a textbook for graduate-level courses in mathematics, biomedical science and engineering, biology, biophysics, biochemistry, medicine, and engineering.

Nonlinear Partial Differential Equations with Applications

Nonlinear Partial Differential Equations with Applications
  • Author : Tomáš Roubíček
  • Publisher : Springer Science & Business Media
  • Release Date : 2013-01-13
  • Total pages : 476
  • ISBN : 9783034805131
  • File Size : 55,7 Mb
  • Total Download : 498
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This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition leads the reader through the general theory based on abstract (pseudo-) monotone or accretive operators as fast as possible towards the analysis of concrete differential equations, which have specific applications in continuum (thermo-) mechanics of solids and fluids, electrically (semi-) conductive media, modelling of biological systems, or in mechanical engineering. Selected parts are mainly an introduction into the subject while some others form an advanced textbook. The second edition simplifies and extends the exposition at particular spots and augments the applications especially towards thermally coupled systems, magnetism, and more. The intended audience is graduate and PhD students as well as researchers in the theory of partial differential equations or in mathematical modelling of distributed parameter systems. ------ The monograph contains a wealth of material in both the abstract theory of steady-state or evolution equations of monotone and accretive type and concrete applications to nonlinear partial differential equations from mathematical modeling. The organization of the material is well done, and the presentation, although concise, is clear, elegant and rigorous. (...) this book is a notable addition to the existing literature. Also, it certainly will prove useful to engineers, physicists, biologists and other scientists interested in the analysis of (...) nonlinear differential models of the real world. (Mathematical Reviews)

Partial Differential Equations

Partial Differential Equations
  • Author : Michael Shearer,Rachel Levy
  • Publisher : Princeton University Press
  • Release Date : 2015-03-01
  • Total pages : 288
  • ISBN : 9781400866601
  • File Size : 30,6 Mb
  • Total Download : 716
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An accessible yet rigorous introduction to partial differential equations This textbook provides beginning graduate students and advanced undergraduates with an accessible introduction to the rich subject of partial differential equations (PDEs). It presents a rigorous and clear explanation of the more elementary theoretical aspects of PDEs, while also drawing connections to deeper analysis and applications. The book serves as a needed bridge between basic undergraduate texts and more advanced books that require a significant background in functional analysis. Topics include first order equations and the method of characteristics, second order linear equations, wave and heat equations, Laplace and Poisson equations, and separation of variables. The book also covers fundamental solutions, Green's functions and distributions, beginning functional analysis applied to elliptic PDEs, traveling wave solutions of selected parabolic PDEs, and scalar conservation laws and systems of hyperbolic PDEs. Provides an accessible yet rigorous introduction to partial differential equations Draws connections to advanced topics in analysis Covers applications to continuum mechanics An electronic solutions manual is available only to professors An online illustration package is available to professors

Handbook of First-Order Partial Differential Equations

Handbook of First-Order Partial Differential Equations
  • Author : Andrei D. Polyanin,Valentin F. Zaitsev,Alain Moussiaux
  • Publisher : CRC Press
  • Release Date : 2001-11-15
  • Total pages : 522
  • ISBN : 041527267X
  • File Size : 30,6 Mb
  • Total Download : 937
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This book contains about 3000 first-order partial differential equations with solutions. New exact solutions to linear and nonlinear equations are included. The text pays special attention to equations of the general form, showing their dependence upon arbitrary functions. At the beginning of each section, basic solution methods for the corresponding types of differential equations are outlined and specific examples are considered. It presents equations and their applications, including differential geometry, nonlinear mechanics, gas dynamics, heat and mass transfer, wave theory and much more. This handbook is an essential reference source for researchers, engineers and students of applied mathematics, mechanics, control theory and the engineering sciences.

Partial Differential Equations and Boundary-Value Problems with Applications

Partial Differential Equations and Boundary-Value Problems with Applications
  • Author : Mark A. Pinsky
  • Publisher : American Mathematical Soc.
  • Release Date : 2011
  • Total pages : 545
  • ISBN : 9780821868898
  • File Size : 40,5 Mb
  • Total Download : 495
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Building on the basic techniques of separation of variables and Fourier series, the book presents the solution of boundary-value problems for basic partial differential equations: the heat equation, wave equation, and Laplace equation, considered in various standard coordinate systems--rectangular, cylindrical, and spherical. Each of the equations is derived in the three-dimensional context; the solutions are organized according to the geometry of the coordinate system, which makes the mathematics especially transparent. Bessel and Legendre functions are studied and used whenever appropriate throughout the text. The notions of steady-state solution of closely related stationary solutions are developed for the heat equation; applications to the study of heat flow in the earth are presented. The problem of the vibrating string is studied in detail both in the Fourier transform setting and from the viewpoint of the explicit representation (d'Alembert formula). Additional chapters include the numerical analysis of solutions and the method of Green's functions for solutions of partial differential equations. The exposition also includes asymptotic methods (Laplace transform and stationary phase). With more than 200 working examples and 700 exercises (more than 450 with answers), the book is suitable for an undergraduate course in partial differential equations.

Applications of Symmetry Methods to Partial Differential Equations

Applications of Symmetry Methods to Partial Differential Equations
  • Author : George W. Bluman,Alexei F. Cheviakov,Stephen Anco
  • Publisher : Springer Science & Business Media
  • Release Date : 2009-10-30
  • Total pages : 398
  • ISBN : 9780387680286
  • File Size : 50,7 Mb
  • Total Download : 455
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This is an acessible book on the advanced symmetry methods for differential equations, including such subjects as conservation laws, Lie-Bäcklund symmetries, contact transformations, adjoint symmetries, Nöther's Theorem, mappings with some modification, potential symmetries, nonlocal symmetries, nonlocal mappings, and non-classical method. Of use to graduate students and researchers in mathematics and physics.

Semigroups of Linear Operators and Applications to Partial Differential Equations

Semigroups of Linear Operators and Applications to Partial Differential Equations
  • Author : Amnon Pazy
  • Publisher : Springer Science & Business Media
  • Release Date : 2012-12-06
  • Total pages : 282
  • ISBN : 9781461255611
  • File Size : 19,7 Mb
  • Total Download : 922
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Since the characterization of generators of C0 semigroups was established in the 1940s, semigroups of linear operators and its neighboring areas have developed into an abstract theory that has become a necessary discipline in functional analysis and differential equations. This book presents that theory and its basic applications, and the last two chapters give a connected account of the applications to partial differential equations.

Harmonic Analysis, Partial Differential Equations and Applications

Harmonic Analysis, Partial Differential Equations and Applications
  • Author : Sagun Chanillo,Bruno Franchi,Guozhen Lu,Carlos Perez,Eric T. Sawyer
  • Publisher : Birkhäuser
  • Release Date : 2017-02-20
  • Total pages : 301
  • ISBN : 9783319527420
  • File Size : 17,7 Mb
  • Total Download : 844
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This collection of articles and surveys is devoted to Harmonic Analysis, related Partial Differential Equations and Applications and in particular to the fields of research to which Richard L. Wheeden made profound contributions. The papers deal with Weighted Norm inequalities for classical operators like Singular integrals, fractional integrals and maximal functions that arise in Harmonic Analysis. Other papers deal with applications of Harmonic Analysis to Degenerate Elliptic equations, variational problems, Several Complex variables, Potential theory, free boundaries and boundary behavior of functions.

Optimal Control of Partial Differential Equations

Optimal Control of Partial Differential Equations
  • Author : Fredi Tröltzsch
  • Publisher : American Mathematical Soc.
  • Release Date : 2010
  • Total pages : 399
  • ISBN : 9780821849040
  • File Size : 9,8 Mb
  • Total Download : 835
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Download Optimal Control of Partial Differential Equations in PDF, Epub, and Kindle

"Optimal control theory is concerned with finding control functions that minimize cost functions for systems described by differential equations. The methods have found widespread applications in aeronautics, mechanical engineering, the life sciences, and many other disciplines. This book focuses on optimal control problems where the state equation is an elliptic or parabolic partial differential equation. Included are topics such as the existence of optimal solutions, necessary optimality conditions and adjoint equations, second-order sufficient conditions, and main principles of selected numerical techniques. It also contains a survey on the Karush-Kuhn-Tucker theory of nonlinear programming in Banach spaces. The exposition begins with control problems with linear equations, quadratic cost functions and control constraints. To make the book self-contained, basic facts on weak solutions of elliptic and parabolic equations are introduced. Principles of functional analysis are introduced and explained as they are needed. Many simple examples illustrate the theory and its hidden difficulties. This start to the book makes it fairly self-contained and suitable for advanced undergraduates or beginning graduate students. Advanced control problems for nonlinear partial differential equations are also discussed. As prerequisites, results on boundedness and continuity of solutions to semilinear elliptic and parabolic equations are addressed. These topics are not yet readily available in books on PDEs, making the exposition also interesting for researchers. Alongside the main theme of the analysis of problems of optimal control, Tr'oltzsch also discusses numerical techniques. The exposition is confined to brief introductions into the basic ideas in order to give the reader an impression of how the theory can be realized numerically. After reading this book, the reader will be familiar with the main principles of the numerical analysis of PDE-constrained optimization."--Publisher's description.

Partial Differential Equations

Partial Differential Equations
  • Author : Walter A. Strauss
  • Publisher : John Wiley & Sons
  • Release Date : 2007-12-21
  • Total pages : 468
  • ISBN : 9780470054567
  • File Size : 31,5 Mb
  • Total Download : 888
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Partial Differential Equations presents a balanced and comprehensive introduction to the concepts and techniques required to solve problems containing unknown functions of multiple variables. While focusing on the three most classical partial differential equations (PDEs)—the wave, heat, and Laplace equations—this detailed text also presents a broad practical perspective that merges mathematical concepts with real-world application in diverse areas including molecular structure, photon and electron interactions, radiation of electromagnetic waves, vibrations of a solid, and many more. Rigorous pedagogical tools aid in student comprehension; advanced topics are introduced frequently, with minimal technical jargon, and a wealth of exercises reinforce vital skills and invite additional self-study. Topics are presented in a logical progression, with major concepts such as wave propagation, heat and diffusion, electrostatics, and quantum mechanics placed in contexts familiar to students of various fields in science and engineering. By understanding the properties and applications of PDEs, students will be equipped to better analyze and interpret central processes of the natural world.

Nonlinear Partial Differential Equations for Future Applications

Nonlinear Partial Differential Equations for Future Applications
  • Author : Shigeaki Koike,Hideo Kozono,Takayoshi Ogawa,Shigeru Sakaguchi
  • Publisher : Springer Nature
  • Release Date : 2021-04-16
  • Total pages : 261
  • ISBN : 9789813348226
  • File Size : 48,7 Mb
  • Total Download : 733
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This volume features selected, original, and peer-reviewed papers on topics from a series of workshops on Nonlinear Partial Differential Equations for Future Applications that were held in 2017 at Tohoku University in Japan. The contributions address an abstract maximal regularity with applications to parabolic equations, stability, and bifurcation for viscous compressible Navier–Stokes equations, new estimates for a compressible Gross–Pitaevskii–Navier–Stokes system, singular limits for the Keller–Segel system in critical spaces, the dynamic programming principle for stochastic optimal control, two kinds of regularity machineries for elliptic obstacle problems, and new insight on topology of nodal sets of high-energy eigenfunctions of the Laplacian. This book aims to exhibit various theories and methods that appear in the study of nonlinear partial differential equations.