| Full text | |
| Author(s): |
Total Authors: 4
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| Affiliation: | [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
Total Affiliations: 2
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| Document type: | Journal article |
| Source: | COMMUNICATIONS ON PURE AND APPLIED ANALYSIS; v. 19, n. 11, p. 5181-5196, NOV 2020. |
| Web of Science Citations: | 0 |
| Abstract | |
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) | |
| FAPESP's process: | 19/20341-3 - Asymptotic analysis of autonomous and non-autonomous parabolic problems |
| Grantee: | Tito Luciano Mamani Luna |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |
| FAPESP's process: | 18/10997-6 - Robustness of attractors under autonomous or non-autonomous perturbatinos: Structural Stability |
| Grantee: | Alexandre Nolasco de Carvalho |
| Support Opportunities: | Scholarships abroad - Research |
| FAPESP's process: | 18/00065-9 - Gradient structure of skew product semiflows |
| Grantee: | Estefani Moraes Moreira |
| Support Opportunities: | Scholarships in Brazil - Doctorate |