Blow-up of solutions for an integro-differential equation with a nonlinear source
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We study the nonlinear viscoelastic wave equation
utt -Δu + ∫t0 g(t - s) Δu(s)ds = |u|pu,
in a bounded domain, with the initial and Dirichlet boundary conditions. By modifying the method in , we prove that there are solutions, under some conditions on the initial data, which blow up in finite time with nonpositive initial energy as well as positive initial energy. Estimates of the lifespan of solutions are also given.
CitationWu, S. T. (2006). Blow-up of solutions for an integro-differential equation with a nonlinear source. Electronic Journal of Differential Equations, 2006(45), pp. 1-9.
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