On gradient estimates and other qualitative properties of solutions of nonlinear non autonomous parabolic systems

被引：0

作者：

Antontsev, S. ^{[1
]}

Diaz, J. I. ^{[2
]}

机构：

[1] Univ Lisbon, CMAF, P-1699 Lisbon, Portugal

[2] Univ Complutense Madrid, Dept Matemat Aplicada, E-28040 Madrid, Spain

来源：

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS | 2009年 / 103卷 / 01期

关键词：

Uniform gradient estimates; quasilinear parabolic onedimensional systems; uniform L(1)-estimates independent on the spatial domain; EQUATIONS; GAS;

D O I：

10.1007/BF03191851

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove several uniform L(1)-estimates on solutions of a general class of one-dimensional parabolic systems, mainly coupled in the diffusion term, which, in fact, can be of degenerate type. They are uniform in the sense that they don't depend on the coefficients, nor on the size of the spatial domain. The estimates concern the own Solution or/and its spatial gradient. This paper extends some previous results by the authors to the case of nonautonomous coefficients and possibly non homogeneous boundary conditions. Moreover, an application to the asymptotic decay of the L(1)-norm of solutions, as t -> +infinity, is also given.

引用

页码：201 / 214

页数：14