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- W3174656243 abstract "In this paper, we consider an initial-boundary value problem for the following mixed pseudo-parabolic $p(.)$-Laplacian type equation with logarithmic nonlinearity: $$ u_t-Delta u_t-mbox{div}left(leftvert nabla urightvert^{p(.)-2}nabla uright) =|u|^{q(.)-2}uln(|u|), quad (x,t)inOmegatimes(0,+infty),$$ where $Omegasubsetmathbb{R}^n$ is a bounded and regular domain, and the variable exponents $p(.)$ and $q(.)$ satisfy suitable regularity assumptions. By adapting the first-order differential inequality method, we establish a blow-up criterion for the solutions and obtain an upper bound for the blow-up time. In a second moment, we show that blow-up may be prevented under appropriate smallness conditions on the initial datum, in which case we also establish decay estimates in the $H_0^1(Omega)$-norm as $tto+infty$." @default.
- W3174656243 created "2021-07-05" @default.
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- W3174656243 date "2021-06-22" @default.
- W3174656243 modified "2023-09-27" @default.
- W3174656243 title "Blow-up results for a logarithmic pseudo-parabolic $p(.)$-Laplacian type equation" @default.
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