Smoothing effect and asymptotic dynamics of nonautonomous parabolic equations with time-dependent linear operators

Asymptotic Behaviour of Parabolic Nonautonomous Evolution Equations

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...

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....

on the effect of linear & non-linear texts on students comprehension and recalling

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