# American Institute of Mathematical Sciences

September  2009, 25(3): 1003-1032. doi: 10.3934/dcds.2009.25.1003

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

Received  July 2008 Revised  April 2009 Published  August 2009

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.
Citation: A. Rodríguez-Bernal. Perturbation of the exponential type of linear nonautonomous parabolic equations and applications to nonlinear equations. Discrete & Continuous Dynamical Systems - A, 2009, 25 (3) : 1003-1032. doi: 10.3934/dcds.2009.25.1003
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