Compactness and asymptotic behavior in nonautonomous linear parabolic equations with unbounded coefficients in $\R^d$

Details Compactness and asymptotic behavior in nonautonomous linear parabolic equations with unbounded coefficients in $\R^d$ Compactness and asymptotic behavior in nonautonomous linear parabolic equations with unbounded coefficients in $\R^d$

2010-06-08

arxiv.org/abs/1006.1530v1

Mathematics

Analysis of PDEs

Scientific paper

We consider a class of second order linear nonautonomous parabolic equations
in R^d with time periodic unbounded coefficients. We give sufficient conditions
for the evolution operator G(t,s) be compact in C_b(R^d) for t>s, and describe
the asymptotic behavior of G(t,s)f as t-s goes to infinity in terms of a family
of measures mu_s, s in R, solution of the associated Fokker-Planck equation.

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