We prove L2-maximal regularity of the linear non-autonomous evolutionary Cauchy problem \dot u(t) + A(t)u(t) = f(t){\text{ for a}}{\text{.e}}{\text{. }}t \in \left[ {0,T} \right],{\text{ }}u(0) = {u_0}, where the operator A(t) arises from a time depending sesquilinear form a(t, ·, ·) on a Hilbert space H with constant domain V. We prove the maximal regularity in H when these forms are time Lipschitz continuous. We proceed by approximating the problem using the frozen coefficient method developed by El-Mennaoui, Keyantuo, Laasri (2011), El-Mennaoui, Laasri (2013), and Laasri (2012). As a consequence, we obtain an invariance criterion for convex and closed sets of H., Ahmed Sani, Hafida Laasri., and Obsahuje seznam literatury
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).