Blow up for a Cauchy viscoelastic problem with a nonlinear dissipation of cubic convolution type

摘要

In this paper, we consider a Cauchy viscoelastic problem with a nonlinear source of polynomial type and a nonlinear dissipation of cubic convolution type involving a singular kernel. Under suitable conditions on the initial data and the relaxation functions, it is proved that the solution of this particular problem blows up in finite time. Copyright.