Abstract
In this paper we present time-dependent perturbations of second-order non-autonomous abstract Cauchy problems associated to a family of operators with constant domain. We make use of the equivalence to a first-order non-autonomous abstract Cauchy problem in a product space, which we elaborate in full detail. As an application we provide a perturbed non-autonomous wave equation.
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Acknowledgement
Christian Seifert thanks for a very pleasant stay at the University of the Free State, South Africa, where this work was done.
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This work is based on the research supported by the National Research Foundation (Grant numbers: 150417, SRUG220317136). It is acknowledged that opinions, findings and conclusions or recommendations expressed in any publication generated by this supported research is that of the author(s). The National Research Foundation accepts no liability whatsoever in this regard.
This article is based upon work from COST Action 18232 MAT-DYN-NET, supported by COST (European Cooperation in Science and Technology).
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Budde, C., Seifert, C. Perturbations of non-autonomous second-order abstract Cauchy problems. Anal Math (2024). https://doi.org/10.1007/s10476-024-00035-8
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DOI: https://doi.org/10.1007/s10476-024-00035-8