Abstract
The goal of the present paper is to study the viscoelastic wave equation with variable exponents
under initial-boundary value conditions, where the exponents of nonlinearity p(x) and q(x) are given functions. To be more precise, blow-up in finite time is proved, upper and lower bounds of the blow-up time are obtained as well. The global existence of weak solutions is presented, moreover, a general stability of solutions is obtained. This work generalizes and improves earlier results in the literature.
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Acknowledgements
The author would like to express her sincere gratitude to Professor Wenjie Gao and Professor Bin Guo for their support and constant encouragement.
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Liao, M. Study of a Viscoelastic Wave Equation with a Strong Dam** and Variable Exponents. Mediterr. J. Math. 18, 186 (2021). https://doi.org/10.1007/s00009-021-01826-1
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DOI: https://doi.org/10.1007/s00009-021-01826-1