Blow-up of solutions for an integro-differential equation with a nonlinear source

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Date
2006-04-06
Authors
Wu, Shun-Tang
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
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 [15], 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.
Description
Keywords
Blow-up, Life span, Viscoelastic, Integro-differential equation
Citation
Wu, S. T. (2006). Blow-up of solutions for an integro-differential equation with a nonlinear source. <i>Electronic Journal of Differential Equations, 2006</i>(45), pp. 1-9.
URI
https://hdl.handle.net/10877/13918
Collections
Electronic Journal of Differential Equations