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

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


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