Analysis Partial Differential Equations And Applications

Author : Tomás Roubicek
Publisher : Springer Science & Business Media
Page : 405 pages
File Size : 40,9 Mb
Release : 2006-01-17
Category : Mathematics
ISBN : 9783764373979

Get Book

Nonlinear Partial Differential Equations with Applications by Tomás Roubicek Pdf

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.

Author : Michael Shearer,Rachel Levy
Publisher : Princeton University Press
Page : 286 pages
File Size : 42,5 Mb
Release : 2015-03-01
Category : Mathematics
ISBN : 9780691161297

Get Book

Partial Differential Equations by Michael Shearer,Rachel Levy Pdf

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

Author : Piero Bassanini,Alan R. Elcrat
Publisher : Unknown
Page : 456 pages
File Size : 45,6 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 1489918760

Get Book

Theory and Applications of Partial Differential Equations by Piero Bassanini,Alan R. Elcrat Pdf

Author : Peter Markowich
Publisher : Springer Science & Business Media
Page : 210 pages
File Size : 49,6 Mb
Release : 2007-08-06
Category : Mathematics
ISBN : 9783540346463

Get Book

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.

Author : Joël Chaskalovic
Publisher : Springer
Page : 358 pages
File Size : 55,8 Mb
Release : 2014-05-16
Category : Mathematics
ISBN : 9783319035635

Get Book

Mathematical and Numerical Methods for Partial Differential Equations by Joël Chaskalovic Pdf

This self-tutorial offers a concise yet thorough introduction into the mathematical analysis of approximation methods for partial differential equation. A particular emphasis is put on finite element methods. The unique approach first summarizes and outlines the finite-element mathematics in general and then in the second and major part, formulates problem examples that clearly demonstrate the techniques of functional analysis via numerous and diverse exercises. The solutions of the problems are given directly afterwards. Using this approach, the author motivates and encourages the reader to actively acquire the knowledge of finite- element methods instead of passively absorbing the material as in most standard textbooks. This English edition is based on the Finite Element Methods for Engineering Sciences by Joel Chaskalovic.

Author : Sagun Chanillo,Bruno Franchi,Guozhen Lu,Carlos Perez,Eric T. Sawyer
Publisher : Birkhäuser
Page : 301 pages
File Size : 47,5 Mb
Release : 2017-02-20
Category : Mathematics
ISBN : 9783319527420

Get Book

Harmonic Analysis, Partial Differential Equations and Applications by Sagun Chanillo,Bruno Franchi,Guozhen Lu,Carlos Perez,Eric T. Sawyer Pdf

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.

Author : Manfred Kracht,Erwin Kreyszig
Publisher : New York ; Toronto : Wiley
Page : 424 pages
File Size : 51,7 Mb
Release : 1988
Category : Mathematics
ISBN : UCAL:B4406640

Get Book

Methods of Complex Analysis in Partial Differential Equations with Applications by Manfred Kracht,Erwin Kreyszig Pdf

This book is devoted to the development of complex function theoretic methods in partial differential equations and to the study of analytic behaviour of solutions. It presents basic facts of the subject and includes recent results, emphasizing the method of integral operators and the method of differential operators. The first chapter gives a motivation for and the underlying ideas of, the later chapters. Chapters 2 to 7 give a detailed exposition of the basic concepts and fundamental theorems, as well as their most recent development. Chapters 8 to 13 are concerned with the application of the theory to three important classes of differential equations of mathematical physics.

Author : E. C. Zachmanoglou,Dale W. Thoe
Publisher : Courier Corporation
Page : 432 pages
File Size : 51,7 Mb
Release : 2012-04-20
Category : Mathematics
ISBN : 9780486132174

Get Book

Introduction to Partial Differential Equations with Applications by E. C. Zachmanoglou,Dale W. Thoe Pdf

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.

Author : Odile Pons
Publisher : World Scientific
Page : 305 pages
File Size : 40,6 Mb
Release : 2022-12-19
Category : Mathematics
ISBN : 9789811268588

Get Book

Analysis And Differential Equations (Second Edition) by Odile Pons Pdf

The book presents advanced methods of integral calculus and optimization, the classical theory of ordinary and partial differential equations and systems of dynamical equations. It provides explicit solutions of linear and nonlinear differential equations, and implicit solutions with discrete approximations.The main changes of this second edition are: the addition of theoretical sections proving the existence and the unicity of the solutions for linear differential equations on real and complex spaces and for nonlinear differential equations defined by locally Lipschitz functions of the derivatives, as well as the approximations of nonlinear parabolic, elliptic, and hyperbolic equations with locally differentiable operators which allow to prove the existence of their solutions; furthermore, the behavior of the solutions of differential equations under small perturbations of the initial condition or of the differential operators is studied.

Author : Mark A. Pinsky
Publisher : American Mathematical Soc.
Page : 545 pages
File Size : 46,7 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821868898

Get Book

Partial Differential Equations and Boundary-Value Problems with Applications by Mark A. Pinsky Pdf

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.

Author : Andrea Manzoni,Alfio Quarteroni,Sandro Salsa
Publisher : Springer Nature
Page : 507 pages
File Size : 40,9 Mb
Release : 2022-01-01
Category : Mathematics
ISBN : 9783030772260

Get Book

Optimal Control of Partial Differential Equations by Andrea Manzoni,Alfio Quarteroni,Sandro Salsa Pdf

This is a book on optimal control problems (OCPs) for partial differential equations (PDEs) that evolved from a series of courses taught by the authors in the last few years at Politecnico di Milano, both at the undergraduate and graduate levels. The book covers the whole range spanning from the setup and the rigorous theoretical analysis of OCPs, the derivation of the system of optimality conditions, the proposition of suitable numerical methods, their formulation, their analysis, including their application to a broad set of problems of practical relevance. The first introductory chapter addresses a handful of representative OCPs and presents an overview of the associated mathematical issues. The rest of the book is organized into three parts: part I provides preliminary concepts of OCPs for algebraic and dynamical systems; part II addresses OCPs involving linear PDEs (mostly elliptic and parabolic type) and quadratic cost functions; part III deals with more general classes of OCPs that stand behind the advanced applications mentioned above. Starting from simple problems that allow a “hands-on” treatment, the reader is progressively led to a general framework suitable to face a broader class of problems. Moreover, the inclusion of many pseudocodes allows the reader to easily implement the algorithms illustrated throughout the text. The three parts of the book are suitable to readers with variable mathematical backgrounds, from advanced undergraduate to Ph.D. levels and beyond. We believe that applied mathematicians, computational scientists, and engineers may find this book useful for a constructive approach toward the solution of OCPs in the context of complex applications.

Author : Deborah E. Richards
Publisher : Nova Science Publishers
Page : 0 pages
File Size : 40,9 Mb
Release : 2015
Category : Differential equations, Partial
ISBN : 1634826434

Get Book

Partial Differential Equations by Deborah E. Richards Pdf

This book includes research on the Lax-Milgram theorem, which can be used to prove existence and uniqueness of weak solutions to partial differential equations and several examples of its application to relevant boundary value problems are presented. The authors also investigate nonlinear control problems for couple partial differential equations arising from climate and circulation dynamics in the equatorial zone; the integration of partial differential equations (PDE) with the help of non-commutative analysis over octonions and Cayley-Dickson algebras; and the existence and properties of solutions, applications in sequential optimal control with pointwise in time state constraints.

Author : Bernard Dacorogna,Nicola Fusco,Stefan Müller,Vladimir Sverak
Publisher : Springer
Page : 250 pages
File Size : 44,7 Mb
Release : 2017-05-29
Category : Mathematics
ISBN : 9783319545141

Get Book

Vector-Valued Partial Differential Equations and Applications by Bernard Dacorogna,Nicola Fusco,Stefan Müller,Vladimir Sverak Pdf

Collating different aspects of Vector-valued Partial Differential Equations and Applications, this volume is based on the 2013 CIME Course with the same name which took place at Cetraro, Italy, under the scientific direction of John Ball and Paolo Marcellini. It contains the following contributions: The pullback equation (Bernard Dacorogna), The stability of the isoperimetric inequality (Nicola Fusco), Mathematical problems in thin elastic sheets: scaling limits, packing, crumpling and singularities (Stefan Müller), and Aspects of PDEs related to fluid flows (Vladimir Sverák). These lectures are addressed to graduate students and researchers in the field.

Author : Boško S. Jovanović,Endre Süli
Publisher : Springer Science & Business Media
Page : 416 pages
File Size : 53,5 Mb
Release : 2013-10-22
Category : Mathematics
ISBN : 9781447154600

Get Book

Analysis of Finite Difference Schemes by Boško S. Jovanović,Endre Süli Pdf

This book develops a systematic and rigorous mathematical theory of finite difference methods for linear elliptic, parabolic and hyperbolic partial differential equations with nonsmooth solutions. Finite difference methods are a classical class of techniques for the numerical approximation of partial differential equations. Traditionally, their convergence analysis presupposes the smoothness of the coefficients, source terms, initial and boundary data, and of the associated solution to the differential equation. This then enables the application of elementary analytical tools to explore their stability and accuracy. The assumptions on the smoothness of the data and of the associated analytical solution are however frequently unrealistic. There is a wealth of boundary – and initial – value problems, arising from various applications in physics and engineering, where the data and the corresponding solution exhibit lack of regularity. In such instances classical techniques for the error analysis of finite difference schemes break down. The objective of this book is to develop the mathematical theory of finite difference schemes for linear partial differential equations with nonsmooth solutions. Analysis of Finite Difference Schemes is aimed at researchers and graduate students interested in the mathematical theory of numerical methods for the approximate solution of partial differential equations.

Author : Haim Brezis
Publisher : Springer Science & Business Media
Page : 600 pages
File Size : 49,7 Mb
Release : 2010-11-02
Category : Mathematics
ISBN : 9780387709147

Get Book

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.