Finite-Dimensional Reduction of Systems of Nonlinear Diffusion Equations

被引：0
|
作者：
Romanov, A. V. [1 ]
机构：
[1] Natl Res Univ Higher Sch Econ, Sch Appl Math, Moscow 123458, Russia
来源：
MATHEMATICAL NOTES | 2023年 / 113卷 / 1-2期
关键词：
nonlinear parabolic equations; finite-dimensional dynamics on an attractor; inertial manifold; INERTIAL MANIFOLDS; DYNAMICS;
D O I：
10.1134/S0001434623010297
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We present a class of one-dimensional systems of nonlinear parabolic equations for which the phase dynamics at large time can be described by an ODE with a Lipschitz vector field in R-n. In the considered case of the Dirichlet boundary value problem, the sufficient conditions for a finite-dimensional reduction turn out to be much wider than the known conditions of this kind for a periodic situation.
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页码：267 / 273
页数：7
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