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

### Impacto

Rodríguez Bernal, Aníbal (2009) Perturbation of the exponential type of linear nonautonomous parabolic equations and applications to nonlinear equations. Discrete and Continuous Dynamical Systems. Series A., 25 (3). pp. 1003-1032. ISSN 1553-5231

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## Abstract

Let $\Omega$ be a bounded domain in a Euclidean space, with a smooth boundary. The paper deals with the linear non-autonomous model equation $$u_t-\Delta u=C(t,x) \quad (x\in \Omega,\ t>0),$$ where $C(x,t)$ is a given function. Besides, various boundary conditions are imposed. The author suggests sharp qualitative and quantitative conditions to guarantee that the exponential type of the considered 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 obtained results are then applied to the investigation of the asymptotic behavior, both forwards and backwards, of solutions of certain nonautonomous nonlinear equations.

Item Type: Article Parabolic equations; Exponential type; Asymptotic behavior; Perturbations; Nonlinear perturbation; Linear perturbation Sciences > Mathematics > Differential equations 12916 11 Jul 2011 08:16 06 Feb 2014 09:36

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