Trajectory attractor for a reaction-diffusion system with a small diffusion coefficient

被引：0

作者：

Vishik, M. I. ^{[1
]}

Chepyzhov, V. V. ^{[1
]}

机构：

[1] Russian Acad Sci, Kharkevich Inst Informat Transmiss Problems, Moscow 127994, Russia

来源：

DOKLADY MATHEMATICS | 2009年 / 79卷 / 02期

基金：

俄罗斯基础研究基金会;

关键词：

Topology - Galerkin methods - Dynamic models - Navier Stokes equations - Diffusion in liquids;

D O I：

10.1134/S1064562409020215

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A study was conducted to demonstrate a trajectory attractor for a reaction-diffusion system with a small diffusion coefficient. It was demonstrated that trajectory attractors were constructed in weak-topology spaces to analyze the asymptotic behavior of appropriate solutions for many model reaction-diffusion systems. It was demonstrated the method was also effective in studying the three-dimensional Navier-Stokes equations and other dissipative equations of mathematical physics. The existence of weak solutions to problem of finding appropriate solutions for a reaction-diffusion system with a small diffusion coefficient was proved by the Galerkin method. The space K 0+ (N) was introduced by analogy Kδ + (N) := K+(N) to construct a trajectory attractor of the reaction-diffusion system.

引用

页码：227 / 230

页数：4

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