On decay and blow-up of solutions for a singular nonlocal viscoelastic problem with a nonlinear source term
Keywords
Singular nonlocal viscoelastic problem, general decay, blow-up, potential well theoryAbstract
We consider a singular nonlocal viscoelastic problem with a nonlinear source term and a possible damping term. We prove that if the initial data enter into the stable set, the solution exists globally and decays to zero with a more general rate, and if the initial data enter into the unstable set, the solution with nonpositive initial energy as well as positive initial energy blows up in finite time. These are achieved by using the potential well theory, the modified convexity method and the perturbed energy method.Published
2016-10-27
How to Cite
1.
LIU, Wenjun, SUN, Yun and LI, Gang. On decay and blow-up of solutions for a singular nonlocal viscoelastic problem with a nonlinear source term. Topological Methods in Nonlinear Analysis. Online. 27 October 2016. Vol. 49, no. 1, pp. 299 - 323. [Accessed 26 April 2024].
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