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Partial Differential Equations

A unified Hilbert Space Approach

Rainer Picard, Des McGhee (Autoren)

Buch | Hardcover

XVIII, 469 Seiten

2011
De Gruyter (Verlag)
978-3-11-025026-8 (ISBN)

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This book presents a systematic approach to a solution theory for linear partial differential equations developed in a Hilbert space setting based on a Sobolev lattice structure, a simple extension of the well-established notion of a chain (or scale) of Hilbert spaces. The focus on a Hilbert space setting (rather than on an apparently more general Banach space) is not a severe constraint, but rather a highly adaptable and suitable approach providing a more transparent framework for presenting the main issues in the development of a solution theory for partial differential equations. In contrast to other texts on partial differential equations, which consider either specific equation types or apply a collection of tools for solving a variety of equations, this book takes a more global point of view by focusing on the issues involved in determining the appropriate functional analytic setting in which a solution theory can be naturally developed. Applications to many areas of mathematical physics are also presented. The book aims to be largely self-contained. Full proofs to all but the most straightforward results are provided, keeping to a minimum references to other literature for essential material. It is therefore highly suitable as a resource for graduate courses and also for researchers, who will find new results for particular evolutionary systems from mathematical physics.

Rainer Picard, Dresden University of Technology, Germany; Des McGhee, University of Strathclyde, Glasgow, Scotland, UK.

Erscheint lt. Verlag	16.6.2011
Reihe/Serie	De Gruyter Expositions in Mathematics ; 55
Verlagsort	Berlin/Boston
Sprache	englisch
Maße	170 x 240 mm
Gewicht	955 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	evolution equation • hilbert space • Mathematics • Mathematics, Partial Differential Equations, Hilbert Space, Sobolev, Evolution Equation • Mathematics; Partial Differential Equations; Hilbert Space; Sobolev; Evolution Equation • Partial differential equations • Partielle Differenzialgleichungen • Sobolev
ISBN-10	3-11-025026-8 / 3110250268
ISBN-13	978-3-11-025026-8 / 9783110250268
Zustand	Neuware