Asymptotic behavior in time periodic parabolic problems with unbounded coefficients

Asymptotic Behavior in Time Periodic Parabolic Problems with Unbounded Coefficients

We study asymptotic behavior in a class of non-autonomous second order parabolic equations with time periodic unbounded coefficients in R×R. Our results generalize and improve asymptotic behavior results for Markov semigroups having an invariant measure. We also study spectral properties of the realization of the parabolic operator u 7→ A(t)u − ut in suitable L spaces.

L–regularity for Parabolic Operators with Unbounded Time–dependent Coefficients

We establish the maximal regularity for nonautonomous OrnsteinUhlenbeck operators in L-spaces with respect to a family of invariant measures, where p ∈ (1,+∞). This result follows from the maximal L-regularity for a class of elliptic operators with unbounded, time-dependent drift coefficients and potentials acting on L(R ) with Lebesgue measure.

Nonautonomous Kolmogorov Parabolic Equations with Unbounded Coefficients

We study a class of elliptic operators A with unbounded coefficients defined in I × R for some unbounded interval I ⊂ R. We prove that, for any s ∈ I, the Cauchy problem u(s, ·) = f ∈ Cb(R ) for the parabolic equation Dtu = Au admits a unique bounded classical solution u. This allows to associate an evolution family {G(t, s)} with A, in a natural way. We study the main properties of this evolut...

Elliptic and parabolic problems in unbounded domains

We consider elliptic and parabolic problems in unbounded domains. We give general existence and regularity results in Besov spaces and semi-explicit representation formulas via operatorvalued fundamental solutions which turn out to be a powerful tool to derive a series of qualitative results about the solutions. We give a sample of possible applications including asymptotic behavior in the larg...

On Asymptotic Behavior of Stopping Time Problems