Asymptotic behaviour for a semilinear nonlocal equation
We study the semilinear nonlocal equation u t =Ju-u-u p in the whole. First, we prove the global well-posedness for initial conditions. Next, we obtain the long time behaviour of the solutions. We show that different behaviours are possible depending on the exponent p and the kernel J: finite time e...
Guardado en:
| Autor principal: | |
|---|---|
| Publicado: |
2007
|
| Materias: | |
| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09217134_v52_n1-2_p143_Pazoto http://hdl.handle.net/20.500.12110/paper_09217134_v52_n1-2_p143_Pazoto |
| Aporte de: |
| Sumario: | We study the semilinear nonlocal equation u t =Ju-u-u p in the whole. First, we prove the global well-posedness for initial conditions. Next, we obtain the long time behaviour of the solutions. We show that different behaviours are possible depending on the exponent p and the kernel J: finite time extinction for p<1, faster than exponential decay for the linear case p=1, a weakly nonlinear behaviour for p large enough and a decay governed by the nonlinear term when p is greater than one but not so large. © 2007 - IOS Press and the authors. All rights reserved. |
|---|