An Introduction to Partial Differential Equations

Michael Renardy, Robert C. Rogers - Collection Texts in Applied Mathematics

435 pages, parution le 26/01/2004 (2^eme édition)

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Résumé

Partial differential equations are fundamental to the modeling of natural phenomena, arising in every field of science. Consequently, the desire to understand the solutions of these equations has always had a prominent place in the efforts of mathematicians; it has inspired such diverse fields as complex function theory, functional analysis and algebraic topology. Like algebra, topology, and rational mechanics, partial differential equations are a core area of mathematics.

This book aims to provide the background necessary to initiate work on a Ph.D. thesis in PDEs for beginning graduate students. Prerequisites include a truly advanced calculus course and basic complex variables. Lebesgue integration is needed only in Chapter 10, and the necessary tools from functional analysis are developed within the course. The book can be used to teach a variety of different courses.

This new edition features new problems throughout and the problems have been rearranged in each section from simplest to most difficult. New examples have also been added. The material on Sobolev spaces has been rearranged and expanded. A new section on nonlinear variational problems with "Young-measure" solutions appears. The reference section has also been expanded.

Written for:
Graduate students, advanced mathematics students

Sommaire

Introduction
Characteristics
Classification of Characteristics
Conservation Laws and Shocks
Maximum Principles
Distributions
Function Spaces
Sobolev Spaces
Operator Theory
Linear Elliptic Equations
Nonlinear Elliptic Equations
Energy Methods for Evolution Problems
Semigroup Methods
References
Index

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Michael Renardy, Robert C. Rogers
Collection	Texts in Applied Mathematics
Parution	26/01/2004
Édition	2^eme édition
Nb. de pages	435
Format	16 x 24
Couverture	Relié
Poids	745g
Intérieur	Noir et Blanc
EAN13	9780387004440
ISBN13	978-0-387-00444-0