# Partial Differential Equations : A Unified Hilbert Space Approach

Mcghee, Desmond and Picard, R.
(2011)
*Partial Differential Equations : A Unified Hilbert Space Approach.*
de Gruyter Expositions in Mathematics 55
.
De Gruyter.
ISBN 9783110250275

## Abstract

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 (rather than an apparently more general Banach space) setting 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 types of partial differential equations or apply a collection of tools for solving a variety of partial differential equations, this book takes a more global point of view 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 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 for researchers, who will find new results for particular evolutionary system from mathematical physics.

Item type: | Book |
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ID code: | 29433 |

Notes: | e-isbn: 978-3-11-025027-5 |

Keywords: | mathematics, partial differential , equations, Hilbert space, Sobolev, evolution equation, Mathematics, Applied Mathematics |

Subjects: | Science > Mathematics |

Department: | Faculty of Science > Mathematics and Statistics |

Depositing user: | Pure Administrator |

Date Deposited: | 08 Mar 2011 00:22 |

Last modified: | 20 Jun 2016 00:10 |

Related URLs: | |

URI: | http://strathprints.strath.ac.uk/id/eprint/29433 |