On decay and blow-up of solutions for a singular nonlocal viscoelastic problem with a nonlinear source term

Wenjun Liu, Yun Sun, Gang Li

DOI: http://dx.doi.org/10.12775/TMNA.2016.077

Abstract


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.

Keywords


Singular nonlocal viscoelastic problem; general decay; blow-up; potential well theory

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