Perturbation of  the  exponential type of linear nonautonomous  parabolic equations and applications to nonlinear equations

A. Rodríguez-Bernal

doi:10.3934/dcds.2009.25.1003

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2009, Volume 25, Issue 3: 1003-1032. Doi: 10.3934/dcds.2009.25.1003

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Perturbation of the exponential type of linear nonautonomous parabolic equations and applications to nonlinear equations

A. Rodríguez-Bernal^1,

1.
Departamento de Matemática Aplicada, Universidad Complutense de Madrid, Madrid 28040

Received: July 2008

Revised: April 2009

Published: September 2009

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Abstract

In this paper we give some sharp qualitative and quantitative conditions to guarantee that the exponential type of a linear nonautonomous equation is modified by a linear perturbation. No assumption (periodic, almost periodic, quasi periodic etc) is made on the time behavior of the coefficients of the equation or the perturbation.
The results are applied to the study of the asymptotic behavior, both forwards and pullback, of nonautonomous nonlinear equations.

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Mathematics Subject Classification: 35B05, 35B20, 35B35, 35K10, 35K55, 35K57.

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Perturbation of the exponential type of linear nonautonomous parabolic equations and applications to nonlinear equations

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