On the existence of patterns in reaction-diffusion problems with Dirichlet boundary conditions
| Autor: | Maicon Sônego |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Electronic Journal of Qualitative Theory of Differential Equations, Vol 2024, Iss 30, Pp 1-14 (2024) |
| Druh dokumentu: | article |
| ISSN: | 1417-3875 |
| DOI: | 10.14232/ejqtde.2024.1.30 |
| Popis: | Consider a general reaction-diffusion problem, $u_t = \Delta u + f(x, u, u_x)$, on a revolution surface or in an $n$-dimensional ball with Dirichlet boundary conditions. In this work, we provide conditions related to the geometry of the domain and the spatial heterogeneities of the problem that ensure the existence or not of a non-constant stationary stable solution. Several applications are presented, particularly with regard to the Allen–Cahn, Fisher–KPP and sine-Gordon equations. |
| Databáze: | Directory of Open Access Journals |
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