TY - BOOK ID - 77928850 TI - Partial differential equations : a unified Hilbert space approach AU - Picard, R. H. AU - McGhee, D. F. PY - 2011 SN - 1283399938 9786613399939 3110250276 9783110250275 9783110250268 3110250268 9781283399937 6613399930 PB - Berlin ; New York : De Gruyter, DB - UniCat KW - Hilbert space. KW - Differential equations, Partial. KW - Partial differential equations KW - Banach spaces KW - Hyperspace KW - Inner product spaces KW - Evolution Equation. KW - Hilbert Space. KW - Mathematics. KW - Partial Differential Equations. KW - Sobolev. UR - https://www.unicat.be/uniCat?func=search&query=sysid:77928850 AB - 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. ER -