Taira K. Analytic Semigroups and Semilinear Initial BVP 2016 torrent

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A careful and accessible exposition of a functional analytic approach to initial boundary value problems for semilinear parabolic differential equations, with a focus on the relationship between analytic semigroups and initial boundary value problems. This semigroup approach is distinguished by the extensive use of the ideas and techniques characteristic of the recent developments in the theory of pseudo-differential operators, one of the most influential works in the modern history of analysis. Complete with ample illustrations and additional references, this new edition offers both streamlined analysis and better coverage of important examples and applications. A powerful method for the study of elliptic boundary value problems, capable of further extensive development, is provided for advanced undergraduates or beginning graduate students, as well as mathematicians with an interest in functional analysis and partial differential equations.
Introduction and Main Results
Preliminaries from Functional Analysis
Theory of Analytic Semigroups
Sobolev Imbedding Theorems
Lp Theory of Pseudo-Differential Operators
Lp Approach to Elliptic Boundary Value Problems
Proof of Theorem 1.1
Proof of Theorem 1.2
Proof of Theorems 1.3 and 1.4
The Laplace Transform
The Maximum Principle
Vector Bundles