Year: 2011
Journal of Partial Differential Equations, Vol. 24 (2011), Iss. 2 : pp. 140–149
Abstract
We study the nonlinear one-dimensional viscoelastic nonlocal problem: $u_{tt}-\frac{1}{x}(xu_x)_x+ ∫^t_0g(t-s)\frac{1}{x}(xu_x(x,s))_xds=|u|^{p-2}u$, with a nonlocal boundary condition. By the method given in [1, 2], 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 blow-up solutions are also given. We improve a nonexistence result in Mesloub and Messaoudi [3].
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v24.n2.3
Journal of Partial Differential Equations, Vol. 24 (2011), Iss. 2 : pp. 140–149
Published online: 2011-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: Blow-up
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