Lq-functional inequalities and weighted porous media equations

被引：24

作者：

Dolbeault, Jean

Gentil, Ivan ^{[1
]}

Guillin, Arnaud ^{[1
,2
]}

Wang, Feng-Yu ^{[3
,4
]}

机构：

[1] Univ Aix Marseille 1, Lab Anal Topol Probabil, F-13453 Marseille, France

[2] Ecole Cent Marseille, F-13453 Marseille, France

[3] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China

[4] Univ Swansea, Dept Math, Swansea SA2 8PP, W Glam, Wales

来源：

POTENTIAL ANALYSIS | 2008年 / 28卷 / 01期

关键词：

logarithmic Sobolev inequality; poincare inequality; porous media equation; asymptotic behaviour; nonlinear parabolic equations; variance; entropy; weighted Sobolev spaces; large time asymptotics; rate of convergence;

D O I：

10.1007/s11118-007-9066-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Using measure-capacity inequalities we study new functional inequalities, namely Lq-Poincare inequalities Var(mu)(f(q))(1/q) <= integral vertical bar del f vertical bar(2)d nu and L-q- logarithmic Sobolev inequalities Ent(mu)(f(2q))(1/q) <= C-LS integral vertical bar Delta f vertical bar(2) dv for any q is an element of (0, 1]. As a consequence, we establish the asymptotic behavior of the solutions to the so-called weighted porous media equation partial derivative u/partial derivative t = Delta u(m) - del(psi).del u(m) for m >= 1, in terms of L-2-norms and entropies.

引用

页码：35 / 59

页数：25

共 16 条

[1] LOGARITHMIC SOBOLEV INEQUALITIES AND EXPONENTIAL INTEGRABILITY [J].