Global Existence and Blow Up of Solutions in a Cauchy Viscoelastic Problem (Journal of Partial Differential Equations, 2018)
The Cauchy problem for a viscoelastic equation with nonlinear dampingand source terms is considered. We establish the nonexistence result of global solutionswith initial energy controlled above by a critical value by modifying the methodintroduced in a work by Autuori et al. in 2010. Then we establish global existence forarbitrary initial data or the energy in potential well. These improve earlier results inthe literatures.
Keywords: Cauchy problem; viscoelastic equation; global existence; blow up.