## Topological Methods in Nonlinear Analysis

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

Wenjun Liu, Yun Sun, and Gang Li

#### 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.

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 49, Number 1 (2017), 299-323.

Dates
First available in Project Euclid: 11 April 2017

https://projecteuclid.org/euclid.tmna/1491876031

Digital Object Identifier
doi:10.12775/TMNA.2016.077

Mathematical Reviews number (MathSciNet)
MR3635647

Zentralblatt MATH identifier
1370.35063

#### Citation

Liu, Wenjun; Sun, Yun; Li, Gang. On decay and blow-up of solutions for a singular nonlocal viscoelastic problem with a nonlinear source term. Topol. Methods Nonlinear Anal. 49 (2017), no. 1, 299--323. doi:10.12775/TMNA.2016.077. https://projecteuclid.org/euclid.tmna/1491876031

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