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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.Read more
- An effective introduction to three interrelated subjects: analytic semigroups, elliptic boundary value problems, and parabolic initial boundary value problems
- Provides a powerful method for future research
- Presents principal ideas concretely and explicitly so readers can appreciate the profound relationship between functional analysis and partial differential equations in analysis
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- Edition: 2nd Edition
- Date Published: April 2016
- format: Paperback
- isbn: 9781316620861
- length: 348 pages
- dimensions: 228 x 153 x 20 mm
- weight: 0.5kg
- contains: 40 b/w illus.
- availability: Available
Table of Contents
1. Introduction and main results
2. Preliminaries from functional analysis
3. Theory of analytic semigroups
4. Sobolev imbedding theorems
5. Lp theory of pseudo-differential operators
6. Lp approach to elliptic boundary value problems
7. Proof of theorem 1.1
8. Proof of theorem 1.2
9. Proof of theorems 1.3 and 1.4
Appendix A. The Laplace Transform
Appendix B. The Maximum Principle
Appendix C. Vector bundles
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