On the nonexistence of global solutions for wave equations with double damping terms and nonlinear memory

M. Berbiche, M. Terchi

In this work, we consider the Cauchy problem for a wave equations with frictional and displacement dependent damping terms with nonlinear memory in multi-dimensional space $\mathbb{R}^{n}$, $n\geq 1$, we will prove the existence and uniqueness of the local solution and the nonexistence of global weak solutions theorems for any dimension space. 

Tbilisi Mathematical Journal, Vol. 13(2) (2020), pp. 161-178