Tools For Pde

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Tools for PDE

Michael E. Taylor
Tools for PDE Book PDF

Author : Michael E. Taylor
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 40,7 Mb
Release : 2000
Category : Differential equations, Partial
ISBN : 9780821843789

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Tools for PDE by Michael E. Taylor Pdf

Developing three related tools that are useful in the analysis of partial differential equations (PDEs) arising from the classical study of singular integral operators, this text considers pseudodifferential operators, paradifferential operators, and layer potentials.

New Tools for Nonlinear PDEs and Application

Marcello D'Abbicco,Marcelo Rempel Ebert,Vladimir Georgiev,Tohru Ozawa
New Tools for Nonlinear PDEs and Application Book PDF

Author : Marcello D'Abbicco,Marcelo Rempel Ebert,Vladimir Georgiev,Tohru Ozawa
Publisher : Springer
Page : 390 pages
File Size : 46,5 Mb
Release : 2019-05-07
Category : Mathematics
ISBN : 9783030109370

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New Tools for Nonlinear PDEs and Application by Marcello D'Abbicco,Marcelo Rempel Ebert,Vladimir Georgiev,Tohru Ozawa Pdf

This book features a collection of papers devoted to recent results in nonlinear partial differential equations and applications. It presents an excellent source of information on the state-of-the-art, new methods, and trends in this topic and related areas. Most of the contributors presented their work during the sessions "Recent progress in evolution equations" and "Nonlinear PDEs" at the 12th ISAAC congress held in 2017 in Växjö, Sweden. Even if inspired by this event, this book is not merely a collection of proceedings, but a stand-alone project gathering original contributions from active researchers on the latest trends in nonlinear evolution PDEs.

Tools and Problems in Partial Differential Equations

Thomas Alazard,Claude Zuily
Tools and Problems in Partial Differential Equations Book PDF

Author : Thomas Alazard,Claude Zuily
Publisher : Springer Nature
Page : 357 pages
File Size : 52,8 Mb
Release : 2020-10-19
Category : Mathematics
ISBN : 9783030502843

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Tools and Problems in Partial Differential Equations by Thomas Alazard,Claude Zuily Pdf

This textbook offers a unique learning-by-doing introduction to the modern theory of partial differential equations. Through 65 fully solved problems, the book offers readers a fast but in-depth introduction to the field, covering advanced topics in microlocal analysis, including pseudo- and para-differential calculus, and the key classical equations, such as the Laplace, Schrödinger or Navier-Stokes equations. Essentially self-contained, the book begins with problems on the necessary tools from functional analysis, distributions, and the theory of functional spaces, and in each chapter the problems are preceded by a summary of the relevant results of the theory. Informed by the authors' extensive research experience and years of teaching, this book is for graduate students and researchers who wish to gain real working knowledge of the subject.

Variational Techniques for Elliptic Partial Differential Equations

Francisco J. Sayas,Thomas S. Brown,Matthew E. Hassell
Variational Techniques for Elliptic Partial Differential Equations Book PDF

Author : Francisco J. Sayas,Thomas S. Brown,Matthew E. Hassell
Publisher : CRC Press
Page : 477 pages
File Size : 40,9 Mb
Release : 2019-01-16
Category : Mathematics
ISBN : 9780429016196

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Variational Techniques for Elliptic Partial Differential Equations by Francisco J. Sayas,Thomas S. Brown,Matthew E. Hassell Pdf

Variational Techniques for Elliptic Partial Differential Equations, intended for graduate students studying applied math, analysis, and/or numerical analysis, provides the necessary tools to understand the structure and solvability of elliptic partial differential equations. Beginning with the necessary definitions and theorems from distribution theory, the book gradually builds the functional analytic framework for studying elliptic PDE using variational formulations. Rather than introducing all of the prerequisites in the first chapters, it is the introduction of new problems which motivates the development of the associated analytical tools. In this way the student who is encountering this material for the first time will be aware of exactly what theory is needed, and for which problems. Features A detailed and rigorous development of the theory of Sobolev spaces on Lipschitz domains, including the trace operator and the normal component of vector fields An integration of functional analysis concepts involving Hilbert spaces and the problems which can be solved with these concepts, rather than separating the two Introduction to the analytical tools needed for physical problems of interest like time-harmonic waves, Stokes and Darcy flow, surface differential equations, Maxwell cavity problems, etc. A variety of problems which serve to reinforce and expand upon the material in each chapter, including applications in fluid and solid mechanics

PETSc for Partial Differential Equations: Numerical Solutions in C and Python

Ed Bueler
PETSc for Partial Differential Equations Numerical Solutions in C and Python Book PDF

Author : Ed Bueler
Publisher : SIAM
Page : 407 pages
File Size : 47,9 Mb
Release : 2020-10-22
Category : Mathematics
ISBN : 9781611976311

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PETSc for Partial Differential Equations: Numerical Solutions in C and Python by Ed Bueler Pdf

The Portable, Extensible Toolkit for Scientific Computation (PETSc) is an open-source library of advanced data structures and methods for solving linear and nonlinear equations and for managing discretizations. This book uses these modern numerical tools to demonstrate how to solve nonlinear partial differential equations (PDEs) in parallel. It starts from key mathematical concepts, such as Krylov space methods, preconditioning, multigrid, and Newton’s method. In PETSc these components are composed at run time into fast solvers. Discretizations are introduced from the beginning, with an emphasis on finite difference and finite element methodologies. The example C programs of the first 12 chapters, listed on the inside front cover, solve (mostly) elliptic and parabolic PDE problems. Discretization leads to large, sparse, and generally nonlinear systems of algebraic equations. For such problems, mathematical solver concepts are explained and illustrated through the examples, with sufficient context to speed further development. PETSc for Partial Differential Equations addresses both discretizations and fast solvers for PDEs, emphasizing practice more than theory. Well-structured examples lead to run-time choices that result in high solver performance and parallel scalability. The last two chapters build on the reader’s understanding of fast solver concepts when applying the Firedrake Python finite element solver library. This textbook, the first to cover PETSc programming for nonlinear PDEs, provides an on-ramp for graduate students and researchers to a major area of high-performance computing for science and engineering. It is suitable as a supplement for courses in scientific computing or numerical methods for differential equations.

Principles of Partial Differential Equations

Alexander Komech,Andrew Komech
Principles of Partial Differential Equations Book PDF

Author : Alexander Komech,Andrew Komech
Publisher : Springer Science & Business Media
Page : 165 pages
File Size : 46,9 Mb
Release : 2009-10-05
Category : Mathematics
ISBN : 9781441910950

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Principles of Partial Differential Equations by Alexander Komech,Andrew Komech Pdf

This concise book covers the classical tools of Partial Differential Equations Theory in today’s science and engineering. The rigorous theoretical presentation includes many hints, and the book contains many illustrative applications from physics.

Pseudodifferential Operators and Nonlinear PDE

Michael Taylor
Pseudodifferential Operators and Nonlinear PDE Book PDF

Author : Michael Taylor
Publisher : Springer Science & Business Media
Page : 234 pages
File Size : 54,7 Mb
Release : 1991-11-01
Category : Mathematics
ISBN : 0817635955

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Pseudodifferential Operators and Nonlinear PDE by Michael Taylor Pdf

For the past 25 years the theory of pseudodifferential operators has played an important role in many exciting and deep investigations into linear PDE. Over the past decade, this tool has also begun to yield interesting results in nonlinear PDE. This book is devoted to a summary and reconsideration of some used of pseudodifferential operator techniques in nonlinear PDE. The book should be of interest to graduate students, instructors, and researchers interested in partial differential equations, nonlinear analysis in classical mathematical physics and differential geometry, and in harmonic analysis.

A Tutorial on Elliptic PDE Solvers and Their Parallelization

Craig C. Douglas,Gundolf Haase,Ulrich Langer
A Tutorial on Elliptic PDE Solvers and Their Parallelization Book PDF

Author : Craig C. Douglas,Gundolf Haase,Ulrich Langer
Publisher : SIAM
Page : 153 pages
File Size : 46,9 Mb
Release : 2003-01-01
Category : Technology & Engineering
ISBN : 0898718171

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A Tutorial on Elliptic PDE Solvers and Their Parallelization by Craig C. Douglas,Gundolf Haase,Ulrich Langer Pdf

This compact yet thorough tutorial is the perfect introduction to the basic concepts of solving partial differential equations (PDEs) using parallel numerical methods. In just eight short chapters, the authors provide readers with enough basic knowledge of PDEs, discretization methods, solution techniques, parallel computers, parallel programming, and the run-time behavior of parallel algorithms to allow them to understand, develop, and implement parallel PDE solvers. Examples throughout the book are intentionally kept simple so that the parallelization strategies are not dominated by technical details.

Partial Differential Equations

Walter A. Strauss
Partial Differential Equations Book PDF

Author : Walter A. Strauss
Publisher : John Wiley & Sons
Page : 467 pages
File Size : 52,5 Mb
Release : 2007-12-21
Category : Mathematics
ISBN : 9780470054567

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Partial Differential Equations by Walter A. Strauss Pdf

Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.

Applied Partial Differential Equations:

Peter Markowich
Applied Partial Differential Equations Book PDF

Author : Peter Markowich
Publisher : Springer Science & Business Media
Page : 210 pages
File Size : 49,8 Mb
Release : 2007-08-06
Category : Mathematics
ISBN : 9783540346463

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Applied Partial Differential Equations: by Peter Markowich Pdf

This book presents topics of science and engineering which occur in nature or are part of daily life. It describes phenomena which are modelled by partial differential equations, relating to physical variables like mass, velocity and energy, etc. to their spatial and temporal variations. The author has chosen topics representing his career-long interests, including the flow of fluids and gases, granular flows, biological processes like pattern formation on animal skins, kinetics of rarified gases and semiconductor devices. Each topic is presented in its scientific or engineering context, followed by an introduction of applicable mathematical models in the form of partial differential equations.

Partial Differential Equations I

Michael E. Taylor
Partial Differential Equations I Book PDF

Author : Michael E. Taylor
Publisher : Springer Science & Business Media
Page : 673 pages
File Size : 47,6 Mb
Release : 2010-10-29
Category : Mathematics
ISBN : 9781441970558

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Partial Differential Equations I by Michael E. Taylor Pdf

The first of three volumes on partial differential equations, this one introduces basic examples arising in continuum mechanics, electromagnetism, complex analysis and other areas, and develops a number of tools for their solution, in particular Fourier analysis, distribution theory, and Sobolev spaces. These tools are then applied to the treatment of basic problems in linear PDE, including the Laplace equation, heat equation, and wave equation, as well as more general elliptic, parabolic, and hyperbolic equations.The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis.

Partial Differential Equations

T. Hillen,I.E. Leonard,H. van Roessel
Partial Differential Equations Book PDF

Author : T. Hillen,I.E. Leonard,H. van Roessel
Publisher : FriesenPress
Page : 683 pages
File Size : 42,6 Mb
Release : 2019-05-15
Category : Mathematics
ISBN : 9781525550249

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Partial Differential Equations by T. Hillen,I.E. Leonard,H. van Roessel Pdf

Provides more than 150 fully solved problems for linear partial differential equations and boundary value problems. Partial Differential Equations: Theory and Completely Solved Problems offers a modern introduction into the theory and applications of linear partial differential equations (PDEs). It is the material for a typical third year university course in PDEs. The material of this textbook has been extensively class tested over a period of 20 years in about 60 separate classes. The book is divided into two parts. Part I contains the Theory part and covers topics such as a classification of second order PDEs, physical and biological derivations of the heat, wave and Laplace equations, separation of variables, Fourier series, D’Alembert’s principle, Sturm-Liouville theory, special functions, Fourier transforms and the method of characteristics. Part II contains more than 150 fully solved problems, which are ranked according to their difficulty. The last two chapters include sample Midterm and Final exams for this course with full solutions.

Functional Analysis, Sobolev Spaces and Partial Differential Equations

Haim Brezis
Functional Analysis Sobolev Spaces and Partial Differential Equations Book PDF

Author : Haim Brezis
Publisher : Springer Science & Business Media
Page : 600 pages
File Size : 55,9 Mb
Release : 2010-11-02
Category : Mathematics
ISBN : 9780387709147

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Functional Analysis, Sobolev Spaces and Partial Differential Equations by Haim Brezis Pdf

This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.

Input-to-State Stability for PDEs

Iasson Karafyllis,Miroslav Krstic
Input to State Stability for PDEs Book PDF

Author : Iasson Karafyllis,Miroslav Krstic
Publisher : Springer
Page : 287 pages
File Size : 54,8 Mb
Release : 2018-06-07
Category : Technology & Engineering
ISBN : 9783319910116

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Input-to-State Stability for PDEs by Iasson Karafyllis,Miroslav Krstic Pdf

This book lays the foundation for the study of input-to-state stability (ISS) of partial differential equations (PDEs) predominantly of two classes—parabolic and hyperbolic. This foundation consists of new PDE-specific tools. In addition to developing ISS theorems, equipped with gain estimates with respect to external disturbances, the authors develop small-gain stability theorems for systems involving PDEs. A variety of system combinations are considered: PDEs (of either class) with static maps; PDEs (again, of either class) with ODEs; PDEs of the same class (parabolic with parabolic and hyperbolic with hyperbolic); and feedback loops of PDEs of different classes (parabolic with hyperbolic). In addition to stability results (including ISS), the text develops existence and uniqueness theory for all systems that are considered. Many of these results answer for the first time the existence and uniqueness problems for many problems that have dominated the PDE control literature of the last two decades, including—for PDEs that include non-local terms—backstepping control designs which result in non-local boundary conditions. Input-to-State Stability for PDEs will interest applied mathematicians and control specialists researching PDEs either as graduate students or full-time academics. It also contains a large number of applications that are at the core of many scientific disciplines and so will be of importance for researchers in physics, engineering, biology, social systems and others.

Partial Differential Equations in Action

Sandro Salsa,Gianmaria Verzini
Partial Differential Equations in Action Book PDF

Author : Sandro Salsa,Gianmaria Verzini
Publisher : Springer
Page : 431 pages
File Size : 42,7 Mb
Release : 2015-05-30
Category : Mathematics
ISBN : 9783319154169

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Partial Differential Equations in Action by Sandro Salsa,Gianmaria Verzini Pdf

This textbook presents problems and exercises at various levels of difficulty in the following areas: Classical Methods in PDEs (diffusion, waves, transport, potential equations); Basic Functional Analysis and Distribution Theory; Variational Formulation of Elliptic Problems; and Weak Formulation for Parabolic Problems and for the Wave Equation. Thanks to the broad variety of exercises with complete solutions, it can be used in all basic and advanced PDE courses.