Partial Differential Equations

Partial Differential Equations
ISBN-10
0486469190
ISBN-13
9780486469195
Series
Partial Differential Equations
Category
Mathematics
Pages
262
Language
English
Published
2008
Publisher
Courier Corporation
Author
Avner Friedman

Description

This three-part treatment of partial differential equations focuses on elliptic and evolution equations. Largely self-contained, it concludes with a series of independent topics directly related to the methods and results of the preceding sections that helps introduce readers to advanced topics for further study. Geared toward graduate and postgraduate students of mathematics, this volume also constitutes a valuable reference for mathematicians and mathematical theorists. Starting with the theory of elliptic equations and the solution of the Dirichlet problem, the text develops the theory of weak derivatives, proves various inequalities and imbedding problems, and derives smoothness theorems. Part Two concerns evolution equations in Banach space and develops the theory of semigroups. It solves the initial-boundary value problem for parabolic equations and covers backward uniqueness, asymptotic behavior, and lower bounds at infinity. The final section includes independent topics directly related to the methods and results of the previous material, including the analyticity of solutions of elliptic and parabolic equations, asymptotic behavior of solutions of elliptic equations near infinity, and problems in the theory of control in Banach space.

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