Structural stability for scalar reaction-diffusion equations

被引：0
作者：
Lee, Jihoon [1 ]
Pires, Leonardo [2 ]
机构：
[1] Chonnam Natl Univ, Gwangju, South Korea
[2] Univ Estadual Ponta Grossa, Ponta Grossa, Parana, Brazil
来源：
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS | 2023年 / 54期
关键词：
Morse-Smale semiflows; rate of convergence of attractors; structural stability; invariant manifolds; Gromov-Hausdorff distance; ATTRACTORS; CONVERGENCE; SYSTEMS;
D O I：
10.14232/ejqtde.2023.1.54
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we prove the structural stability for a family of scalar reaction-diffusion equations. Our arguments consist of using invariant manifold theorem to reduce the problem to a finite dimension and then, we use the structural stability of Morse-Smale flows in a finite dimension to obtain the corresponding result in infinite dimension. As a consequence, we obtain the optimal rate of convergence of the attractors and estimate the Gromov-Hausdorff distance of the attractors using continuous e-isometries.
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页码：1 / 12
页数：12
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