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Title: Blow up in a semilinear pseudo-parabolic equation with variable exponents
Authors: Messaoudi, Salim A. 
Talahmeh, Ala A. 
Keywords: Pseudo-parabolic equation;Differential equations, Partial;Finite time;Blow up;Differential equations, Partial - Numerical solutions;Weak solutions;Variable-exponents nonlinearity
Issue Date: 2019
Abstract: In this paper, we consider the following pseudo-parabolic equation with variable exponents: ut − u − ut + t 0 g(t − τ )u(x,τ)dτ = |u| p(x)−2u. Under suitable assumptions on the initial datium u0, the relaxation function g and the variable exponents p, we prove that any weak solution, with initial data at arbitrary energy level, blows up in finite time. Keywords Pseudo-parabolic equation · Blow up · Finite time · Weak solutions · Variable-exponents nonlinearity Mathematics Subject Classification 35B44 · 35D30 · 35L70
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