Global attractors of generic reaction diffusion equations under Lipschitz perturbations

Article Mathematics, Applied

Topological stability of Chafee-Infante equations under Lipschitz perturbations of the domain and equation

Jihoon Lee et al.

Summary: This paper studies the dynamics of Chafee-Infante equations under Lipschitz perturbations of the domain and equation. It describes the geometric equivalence between the global attractor A(0) of the Chafee-Infante equation and the global attractors A(eta) of the perturbed systems. Moreover, it shows the topological stability of the equation on its global attractor in the Gromov-Hausdorff sense.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2023)

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Article Mathematics, Applied

Lipschitz perturbations of the Chafee-Infante equation

Leonardo Pires

Summary: In this paper, the authors study Lipschitz perturbations of the Chafee-Infante equation, which is not differentiable. They prove the permanence and stability of equilibrium points and establish a Lipschitz version of the Hartman-Grobman theorem to find a local homeomorphism that maps orbits near each equilibrium point. The authors also demonstrate the continuity of attractors under Lipschitz perturbations.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2023)

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Article Mathematics, Applied

Gromov-Hausdorff stability of reaction diffusion equations with Neumann boundary conditions under perturbations of the domain

Jihoon Lee

Summary: This paper focuses on the continuity of global attractors and the Gromov-Hausdorff stability of reaction diffusion equations with Neumann boundary conditions under perturbations of the domain, assuming that every equilibrium of the system is hyperbolic.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2021)

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Article Mathematics, Applied

GROMOV-HAUSDORFF STABILITY OF REACTION DIFFUSION EQUATIONS WITH ROBIN BOUNDARY CONDITIONS UNDER PERTURBATIONS OF THE DOMAIN AND EQUATION

Jihoon Lee et al.

Summary: This paper establishes the continuity of global attractors and Gromov-Hausdorff stability of reaction diffusion equations with Robin boundary conditions under perturbations, provided that each equilibrium of the unperturbed equation is hyperbolic.

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS (2021)

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Article Mathematics