EXISTENCE AND BLOW UP FOR A NONLINEAR VISCOELASTIC HYPERBOLIC PROBLEM WITH VARIABLE EXPONENTS
Abstract
Our aim in this paper is to establish the weak existence theorem andfind under suitable assumptions sufficient conditions on $m, p$ andthe initial data for which the blow up takes place for the followingboundary value problem:$$|u_t|^{\rho}u_{tt}-\Delta u-\Deltau_{tt}+\displaystyle\int_{0}^{t}g(t-s)\Delta u(s)ds+|u_{t}|^{m(x)-2}u_{t}=|u|^{p(x)-2}u.$$This paper extends some of the results obtained by the authors and it is focused on new results which are consequence of the presence ofvariable exponents.
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DOI: https://doi.org/10.22190/FUMI2003647M
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