Biblioteca de la Universidad Complutense de Madrid

Pullback attractors and extremal complete trajectories for non-autonomous reaction-diffusion problems

Impacto



Rodríguez Bernal, Aníbal y Vidal López, Alejandro y Robinson, James C. (2007) Pullback attractors and extremal complete trajectories for non-autonomous reaction-diffusion problems. Journal of Differential Equations, 238 (2). 289-337 . ISSN 0022-0396

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URL Oficial: http://www.sciencedirect.com/science/journal/00220396



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.


Tipo de documento:Artículo
Palabras clave:Pullback attractors; Extremal complete trajectories; Reaction-diffusion equation; Evolution operator; Exponentially stable; Non-autonomous logistic equation
Materias:Ciencias > Matemáticas > Ecuaciones diferenciales
Código ID:12776
Depositado:27 May 2011 08:31
Última Modificación:06 Feb 2014 09:32

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