Existence, uniqueness and attractivity properties of positive complete trajectories for  non-autonomous  reaction-diffusion problems

Aníbal Rodríguez-Bernal; Alejandro Vidal–López

doi:10.3934/dcds.2007.18.537

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2007, Volume 18, Issue 2&3: 537-567. Doi: 10.3934/dcds.2007.18.537

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Existence, uniqueness and attractivity properties of positive complete trajectories for non-autonomous reaction-diffusion problems

Aníbal Rodríguez-Bernal^1, and
Alejandro Vidal–López^2,

1.
Universidad Complutense de Madrid, Facultad de Ciencias Matemática, Matemática Aplicada, 28040, Madrid
2.
Depto. Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid

Received: February 28, 2006

Revised: May 31, 2006

Published: May 2007

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Abstract

We give conditions for the existence of a unique positive complete trajectories for non-autonomous reaction-diffusion equations. Also, attraction properties of the unique complete trajectory is obtained in a pullback sense and also forward in time. As an example, a non-autonomous logistic equation is considered.

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Mathematics Subject Classification: Primary: 35K57; Secondary: 35B35.

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