Morse index of steady-states to the SKT model with Dirichlet boundary conditions

Fuente: arXiv
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Main Authors: Kuto, Kousuke, Sato, Homare
Format: Preprint
Published: 2023
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author Kuto, Kousuke
Sato, Homare
author_facet Kuto, Kousuke
Sato, Homare
contents This paper deals with the stability analysis for steady-states perturbed by the full cross-diffusion limit of the SKT model with Dirichlet boundary conditions. Our previous result showed that positive steady-states consist of the branch of small coexistence type bifurcating from the trivial solution and the branches of segregation type bifurcating from points on the branch of small coexistence type. This paper shows the Morse index of steady-states on the branches and constructs the local unstable manifold around each steady-state of which the dimension is equal to the Morse index.
format Preprint
id arxiv_https___arxiv_org_abs_2312_16107
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Morse index of steady-states to the SKT model with Dirichlet boundary conditions
Kuto, Kousuke
Sato, Homare
Analysis of PDEs
92C15, 35B32, 35B35, 92D25, 35B20
This paper deals with the stability analysis for steady-states perturbed by the full cross-diffusion limit of the SKT model with Dirichlet boundary conditions. Our previous result showed that positive steady-states consist of the branch of small coexistence type bifurcating from the trivial solution and the branches of segregation type bifurcating from points on the branch of small coexistence type. This paper shows the Morse index of steady-states on the branches and constructs the local unstable manifold around each steady-state of which the dimension is equal to the Morse index.
title Morse index of steady-states to the SKT model with Dirichlet boundary conditions
topic Analysis of PDEs
92C15, 35B32, 35B35, 92D25, 35B20
url https://arxiv.org/abs/2312.16107