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maximal regularity; on-autonomous evolution equation; stability for linear evolution equation; integrability for linear evolution equation
We study stability and integrability of linear non-autonomous evolutionary Cauchy-problem $$ ({\rm P}) \begin {cases} \dot {u}(t)+A(t)u(t)=f(t)\quad t\text {-a.e. on} [0,\tau ], u(0)=0, \end {cases} $$ where $A\colon [0,\tau ]\to \mathcal {L}(X,D)$ is a bounded and strongly measurable function and $X$, $D$ are Banach spaces such that $D\underset {d}\to {\hookrightarrow }X$. Our main concern is to characterize $L^p$-maximal regularity and to give an explicit approximation of the problem (P).
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