Attractors of partial differential evolution equations in an unbounded domain

Autor:	M. I. Vishik, A. V. Babin
Rok vydání:	1990
Předmět:	Stochastic partial differential equation Sobolev space Pure mathematics Nonlinear system Partial differential equation Distributed parameter system General Mathematics Mathematical analysis Attractor Domain (mathematical analysis) Mathematics Numerical partial differential equations
Zdroj:	Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 116:221-243
ISSN:	1473-7124 0308-2105
DOI:	10.1017/s0308210500031498
Popis:	SynopsisThere is a large number of papers in which attractors of parabolic reaction-diffusion equations in bounded domains are investigated. In this paper, these equations are considered in the whole unbounded space, and a theory of attractors of such equations is built. While investigating these equations, specific difficulties arise connected with the noncompactness of operators, with the continuity of their spectra, etc. Therefore some new conditions on nonlinear terms arise. In this paper weighted spaces are widely applied. An important feature of this problem is worth mentioning: namely, properties of semigroups corresponding to equations with solutions in spaces of growing and of decreasing functions essentially differ.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::ec35d5d51e20ba2478f71326fe377200 https://doi.org/10.1017/s0308210500031498 Zobrazit plný text záznamu