Abstract
We consider non-autonomous wave equations
where the operators \({\mathcal{A}(t)}\) and \({\mathcal{B}(t)}\) are associated with time-dependent sesquilinear forms \({\mathfrak{a}(t, ., .)}\) and \({\mathfrak{b}}\) defined on a Hilbert space H with the same domain V. The initial values satisfy \({u_0 \in V}\) and \({u_1 \in H}\). We prove well-posedness and maximal regularity for the solution both in the spaces V′ and H. We apply the results to non-autonomous Robin-boundary conditions and also use maximal regularity to solve a quasilinear problem.
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Dier, D., Ouhabaz, E.M. Maximal Regularity for Non-Autonomous Second Order Cauchy Problems. Integr. Equ. Oper. Theory 78, 427–450 (2014). https://doi.org/10.1007/s00020-013-2109-6
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DOI: https://doi.org/10.1007/s00020-013-2109-6