Parabolic boundary value problems
type: Item
instance of: scholarly article
title: Parabolic boundary value problems
zbMATH Open document ID: 0893.35001
author: S. D. Eĭdel'man
author: Nicolae Jitaraşu
published in: Operator Theory: Advances and Applications
publication date: 1998-02-25T00:00:00Z
review text: The present monograph is devoted to the theory of general parabolic boundary value problems. In the first chapter the authors define the basic notions at the origin of the theory of parabolic problems and give various examples of illustrative and descriptive character. Chapters II to V are devoted to detailed and systematic exposition of the \(L_2\)-theory of parabolic boundary value problems in Hilbert spaces of smooth functions and distributions of arbitrary finite order and with some natural applications of the theory. The parabolic problem is related with the scale of pairs \(\{U_s, F_s\}\) of Hilbert spaces of distributions depending on the real parameter \(s\) so that the operator of the problem realizes an isomorphism between the spaces \(U_s\) and \(F_s\). For sufficiently large \(s\) the solution is a usual classical solution of the boundary value problem. In Chapter VI the authors give a survey of results to Cauchy problems and boundary value problems in the traditional spaces of smooth functions. Special attention is paid to a detailed analysis of examples illustrating and complementing the results formulated. One can read the chapter alone, skipping the previous chapters. Chapter VII is devoted to theorems on stabilization of solutions of parabolic problems. The monograph is very useful both for graduate and post-graduate students, and for scientific researchers whose interests lie in the field of differential equations. For the Russian original (1992) see Zbl 0855.35002.
Mathematics Subject Classification ID: 35-02
Mathematics Subject Classification ID: 35K20
Mathematics Subject Classification ID: 35K35
Mathematics Subject Classification ID: 35K51
Mathematics Subject Classification ID: 35K52
Mathematics Subject Classification ID: 35B35
zbMATH DE Number: 1120673
zbMATH Keywords: Hilbert spaces of smooth functions
zbMATH Keywords: Hilbert spaces of distributions
zbMATH Keywords: stabilization of solutions
MaRDI profile type: Publication
Recommended article: Q4897366
Recommended article: Q5751280
Recommended article: Q5520962
Recommended article: Linear second-order partial differential equations of the parabolic type
Recommended article: On the first boundary value problem for quasilinear parabolic equations with two independent variables
Recommended article: Method of investigating boundary-value problems in distribution spaces and boundary integral equations
Recommended article: Q5748247
Recommended article: Q4705357
Recommended article: Q4354424
Recommended article: Q2933467
description: scientific article; zbMATH DE number 1120673