Explicit decay estimates for solutions to nonlinear parabolic systems

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Abstract

The aim of this paper is to investigate a class of nonlinear parabolic systems with initial and boundary values of Dirichlet type, when the nonlinearities depend on the gradient of the solution. Sufficient conditions on data are established in order to preclude blow up and to deduce that the solution decays exponentially in time. Moreover, an upper bound of its gradient is derived.

Mathematics Subject Classification (2000)

35K50 35B40 35B50 

Keywords

Nonlinear parabolic systems Maximum principle Decay bounds 
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Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  1. 1.Dipartimento di Matematica e InformaticaUniversitá di CagliariCagliariItaly

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