| Título: | Pullback attractors and extremal complete trajectories for non-autonomous reaction-diffusion problems |
| Autores: | Rodríguez Bernal, Aníbal ; Vidal López, Alejandro ; Robinson, James C. |
| Tipo de documento: | texto impreso |
| Editorial: | Elsevier, 2007 |
| Dimensiones: | application/pdf |
| Nota general: | info:eu-repo/semantics/openAccess |
| Idiomas: | |
| Palabras clave: | Estado = Publicado , Materia = Ciencias: Matemáticas: Ecuaciones diferenciales , Tipo = Artículo |
| Resumen: |
We analyse the dynamics of the non-autonomous nonlinear reaction–diffusion equation ut ?_u = f (t,x,u), subject to appropriate boundary conditions, proving the existence of two bounding complete trajectories, one maximal and one minimal. Our main assumption is that the nonlinear term satisfies a bound of the form f (t,x,u)u _ C(t, x)|u|2 + D(t, x)|u|, where the linear evolution operator associated with _ + C(t, x) is exponentially stable. As an important step in our argument we give a detailed analysis of the exponential stability properties of the evolution operator for the non-autonomous linear problem ut ? _u = C(t, x)u between different Lp spaces. |
| En línea: | https://eprints.ucm.es/id/eprint/12776/1/2005pullback-23.pdf |
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