Convergence to travelling waves for quasilinear Fisher–KPP type equations
We consider the Cauchy problem ut = ϕ(u)xx + ψ(u), (t, x) ∈ R+ × R, u(0, x) = u0(x), x ∈ R, when the increasing function ϕ satisfies that ϕ(0) = 0 and the equation may degenerate at u = 0 (in the case of ϕ� (0) = 0). We consider the case of u0 ∈ L∞(R), 0 u0(x) 1 a.e. x ∈ R and the special case of ψ(...
| Autores: | , |
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| Formato: | artículo |
| Fecha de publicación: | 2012 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/44510 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/44510 |
| Access Level: | acceso abierto |
| Palavra-chave: | 517.9 Kolmogorov Petrovsky and Piscunov equation Travelling waves Asymptotic convergence Ecuaciones diferenciales 1202.07 Ecuaciones en Diferencias |
| Resumo: | We consider the Cauchy problem ut = ϕ(u)xx + ψ(u), (t, x) ∈ R+ × R, u(0, x) = u0(x), x ∈ R, when the increasing function ϕ satisfies that ϕ(0) = 0 and the equation may degenerate at u = 0 (in the case of ϕ� (0) = 0). We consider the case of u0 ∈ L∞(R), 0 u0(x) 1 a.e. x ∈ R and the special case of ψ(u) = u − ϕ(u). We prove that the solution approaches the travelling wave solution (with speed c = 1), spreading either to the right or to the left, or to the two travelling waves moving in opposite directions. |
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