A NON-AUTONOMOUS BIFURCATION PROBLEM FOR A NON-LOCAL SCALAR ONE-DIMENSIONAL PARABOLIC EQUATION

Autor(es)

Li, Yanan ^[1] ; Carvalho, Alexandre N. ^[2] ; Luna, Tito L. M. ^[2] ; Moreira, Estefani M. ^[2]

Afiliação do(s) autor(es)

^[1] Harbin Engn Univ, Coll Math Sci, Harbin 150001 - Peoples R China

^[2] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Campus Sao Carlos, BR-668 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS; v. 19, n. 11, p. 5181-5196, NOV 2020.
• Citações Web of Science: 0

Resumo

In this paper we study the asymptotic behaviour of solutions for a non-local non-autonomous scalar quasilinear parabolic problem in one space dimension. Our aim is to give a fairly complete description of the forward asymptotic behaviour of solutions for models with Kirchhoff type diffusion. In the autonomous case we use the gradient structure, symmetry properties and comparison results to obtain a sequence of bifurcations of equilibria, analogous to what is seen in the local diffusivity case. We provide conditions so that the autonomous problem admits at most one positive equilibrium and analyse the existence of sign changing equilibria. Also using symmetry and the comparison results (developed here) we construct what is called non-autonomous equilibria to describe part of the asymptotics of the associated non-autonomous non-local parabolic problem. (AU)

• Processo FAPESP: 19/20341-3 - Análise assintótica de problemas parabólicos autônomos e não-autônomos
• Beneficiário: Tito Luciano Mamani Luna
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 18/10997-6 - Robusteza de atratores sob perturbações autônomas ou não-autônomas: Estabilidade estrutural
• Beneficiário: Alexandre Nolasco de Carvalho
• Modalidade de apoio: Bolsas no Exterior - Pesquisa
• Processo FAPESP: 18/00065-9 - Estrutura gradiente de semifluxos skew product
• Beneficiário: Estefani Moraes Moreira
• Modalidade de apoio: Bolsas no Brasil - Doutorado