PDE Seminar Abstracts

The aim of this talk is to discuss some recent progress on a problem of J.L. Lions concerning maximal regularity for evolution equations

$${u}^{\prime}\left(t\right)+A\left(t\right)u\left(t\right)=f\left(t\right),\phantom{\rule{2em}{0ex}}u\left(0\right)={u}_{0}.$$

Unlike the autonomous case (where $A\left(t\right)=A$) in which one always has maximal regularity in the Hilbert space setting, the non-autonomous equations may not enjoy this property. We describe some positive and negative results on this problem.

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