Partial Differential Equations
A Unified Hilbert Space Approach
AUTHOR: Picard, R. H. and McGhee, Des
PUBLISHER: Walter De Gruyter Incorporated
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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 is 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. This global point of view is taken by focussing on the issues involved in determining the appropriate functional analytic setting in which a solution theory can naturally be developed. Applications to many areas of mathematical physics are presented.
The book aims to be a largely self-contained. Full proofs to all but the most straightforward results are provided. It is therefore highly suitable as a resource for graduate courses and for researchers, who will find new results for particular evolutionary system from mathematical physics.
PUBLICATION DATE: 6/16/2011