Nonautonomous Kolmogorov parabolic equations with unbounded coefficients

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...

Nonautonomous Parabolic Equations Involving Measures

where Ω ⊂ R and Γ is the boundary of Ω. In this case μΩ is a bounded Radon measure on Ω× J and μΓ is such a measure on Γ× J . In [10] the semilinear analogues of (0.1) and (0.2), where μ and (μΩ, μΓ), respectively, may also depend nonlinearly and nonlocally on the unknown solution u, are investigated. Based on the results of [5], general existence, uniqueness, and continuity theorems are proved...

Parabolic Equations with Measurable Coefficients

We investigate the unique solvability of second order parabolic equations in non-divergence form in W 1,2 p ((0, T ) × R), p ≥ 2. The leading coefficients are only measurable in either one spatial variable or time and one spatial variable. In addition, they are VMO (vanishing mean oscillation) with respect to the remaining variables.

Nonautonomous Parabolic Equations Involving Measures H

In the first part of this paper, we study abstract parabolic evolution equations involving Banach space-valued measures. These results are applied in the second part to second-order parabolic systems under minimal regularity hypotheses on the coefficients. DOI: https://doi.org/10.1007/s10958-005-0376-8 Posted at the Zurich Open Repository and Archive, University of Zurich ZORA URL: https://doi....

Asymptotic Behaviour of Parabolic Nonautonomous Evolution Equations