Gromov-Hausdorff stability of reaction diffusion equations with Robin boundary conditions under perturbations of the domain and equation

Jihoon Lee; Nguyen Thanh Nguyen

doi:10.3934/cpaa.2021020

Article Contents

2021, Volume 20, Issue 3: 1263-1296. Doi: 10.3934/cpaa.2021020

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Gromov-Hausdorff stability of reaction diffusion equations with Robin boundary conditions under perturbations of the domain and equation

Jihoon Lee^1, , and
Nguyen Thanh Nguyen^2,

1.
Department of Mathematics, Sungkyunkwan University, Suwon 16419, Korea
2.
Department of Mathematics, Chungnam National University, Daejeon 34134, Korea

^* Corresponding author
^* Corresponding author

Received: July 31, 2020

Revised: November 30, 2020

Early access: February 2021

Published: March 2021

The first author is supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF- 2019R1A6A3A01091340) and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) No. 2015R1A3A2031159

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Abstract

In this paper, we prove the continuity of global attractors and the Gromov-Hausdorff stability of reaction diffusion equations with Robin boundary conditions under perturbations of the domain and equation if every equilibrium of the unperturbed equation is hyperbolic.

Keywords:

Gromov-Haudorff distance,
reaction diffusion equations,
Robin boundary condition,
perturbation of the domain and equation,
global attractors.

Mathematics Subject Classification: Primary: 35B40, 35B41, 35K20; Secondary: 58D25.

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References

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