Linear parabolic equations in locally uniform spaces

被引：70

作者：

Arrieta, JM ^{[1
]}

Rodriguez-Bernal, A

Cholewa, JW

Dlotko, T

机构：

[1] Univ Complutense Madrid, Dept Matemat Aplicada, Madrid 28040, Spain

[2] Silesian Univ, Inst Math, PL-40007 Katowice, Poland

来源：

MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES | 2004年 / 14卷 / 02期

关键词：

uniform spaces; heat equation; Schrodinger semigroup; analytic semigroups; Lp - L-q estimates; regularizing effect; exponential type;

D O I：

10.1142/S0218202504003234

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We analyze the linear theory of parabolic equations in uniform spaces. We obtain sharp L-p - L-q-type estimates in uniform spaces for heat and Schrodinger semigroups and analyze the regularizing effect and the exponential type of these semigroups. We also deal with general second-order elliptic operators and study the generation of analytic semigoups in uniform spaces.

引用

页码：253 / 293

页数：41

共 36 条

[1] EXISTENCE AND FINITE DIMENSIONALITY OF THE GLOBAL ATTRACTOR FOR EVOLUTION-EQUATIONS ON UNBOUNDED-DOMAINS [J].

ABERGEL, F .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1990, 83 (01) :85-108

[2]

Adams A, 2003, SOBOLEV SPACES

[3] A priori bounds and multiple solutions for superlinear indefinite elliptic problems [J].

Amann, H ;

Lopez-Gomez, J .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1998, 146 (02) :336-374

[4]

AMANN H., 1994, DIFFERENTIAL INTEGRA, V3, P613

[5]

Amann H., 1995, Abstract linear theory, volume89 of Monographs in Mathematics, VI

[6]

Amann H., 1993, FUNCTION SPACES DIFF, P9

[7] ABSORPTION SEMIGROUPS AND DIRICHLET BOUNDARY-CONDITIONS [J].

ARENDT, W ;

BATTY, CJK .

MATHEMATISCHE ANNALEN, 1993, 295 (03) :427-448

[8]

ARENDT W, 1993, DIFFERENTIAL INTEGRA, V6, P1009

[9] Asymptotic behavior and attractors for reaction diffusion equations in unbounded domains [J].

Arrieta, JM ;

Cholewa, JW ;

Dlotko, T ;

Rodríguez-Bernal, A .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2004, 56 (04) :515-554

[10] ATTRACTORS OF PARTIAL-DIFFERENTIAL EVOLUTION-EQUATIONS IN AN UNBOUNDED DOMAIN [J].

BABIN, AV ;

VISHIK, MI .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1990, 116 :221-243

← 1 2 3 4 →