RT Journal Article
T1 Perturbation of the exponential type of linear nonautonomous parabolic equations and applications to nonlinear equations
A1 Rodríguez Bernal, Aníbal
AB 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.
PB American Institute of Mathematical Sciences
SN 1553-5231
YR 2009
FD 2009
LK https://hdl.handle.net/20.500.14352/49706
UL https://hdl.handle.net/20.500.14352/49706
LA eng
NO MTM
NO DGES and Programa de Financiación de Grupos de Investigación
NO CADEDIF
DS Docta Complutense
RD 22 abr 2025