Abstract
We consider evolution equations of the form
where \({\mathcal {A}}(t),\ t\in [0,T],\) are associated with a non-autonomous sesquilinear form \({\mathfrak {a}}(t,\cdot ,\cdot )\) on a Hilbert space H with constant domain \(V\subset H.\) In this note we continue the study of fundamental operator theoretical properties of the solutions. We give a sufficient condition for norm-continuity of evolution families on each spaces V, H and on the dual space \(V'\) of V. The abstract results are applied to a class of equations governed by time dependent Robin boundary conditions on exterior domains and by Schrödinger operator with time dependent potentials.
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Communicated by Markus Haase.
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EL-Mennaoui, O., Laasri, H. A note on the norm-continuity for evolution families arising from non-autonomous forms. Semigroup Forum 100, 451–460 (2020). https://doi.org/10.1007/s00233-019-10076-3
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DOI: https://doi.org/10.1007/s00233-019-10076-3