Critical exponent for damped wave equations with nonlinear memory - Mathematics > Analysis of PDEs

Abstract: We consider the Cauchy problem in $\mathbb{R}^n,$ $n\geq 1,$ for a semilineardamped wave equation with nonlinear memory. Global existence and asymptoticbehavior as $t ightarrow\infty$ of small data solutions have been establishedin the case when $1\leq n\leq3.$ Moreover, we derive a blow-up result undersome positive data in any dimensional space.