Abstract
In this paper, we consider the Cauchy problem in \(\mathbb {R}^n,\) \(n\ge 1,\) for semilinear damped wave equations with space–time dependent potential and nonlinear memory. A blow-up result under some positive data in any dimensional space is obtained. Moreover, the local existence in the energy space is also studied.
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The authors would like to express their thanks to the anonymous referee for his/her useful comments and suggestions concerning the paper. The third author is supported by a grant from the Lebanese University.
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Dannawi, I., Kirane, M. & Fino, A.Z. Finite time blow-up for damped wave equations with space–time dependent potential and nonlinear memory. Nonlinear Differ. Equ. Appl. 25, 38 (2018). https://doi.org/10.1007/s00030-018-0533-7
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DOI: https://doi.org/10.1007/s00030-018-0533-7