Abstract
In this paper, a wave equation of Kirchhoff type of the form
is considered. Under suitable assumptions on the viscoelastic term and initial data, we prove that the solutions blow up at a finite time. Our result improves the previous work by Chen and Liu (IMA J Appl Math 1–29, 2015) in which the authors obtained an exponential growth of solutions where the memory kernel depends on initial energy and we show that it is not necessary to have such a restriction. This also extends the work by Hu et al. (Bound Value Probl 2017:112, 2017) where the relaxation function has not been considered. Some estimates for lower bounds of blowup time are also given.
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Peyravi, A., Tahamtani, F. Upper and Lower Bounds of Blowup Time to a Strongly Damped Wave Equation of Kirchhoff Type with Memory Term and Nonlinear Dissipations. Mediterr. J. Math. 15, 117 (2018). https://doi.org/10.1007/s00009-018-1161-5
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DOI: https://doi.org/10.1007/s00009-018-1161-5