Critical exponent for damped wave equations with nonlinear memory

Details Critical exponent for damped wave equations with nonlinear memory Critical exponent for damped wave equations with nonlinear memory

2010-04-22

arxiv.org/abs/1004.3850v4

Mathematics

Analysis of PDEs

Scientific paper

We consider the Cauchy problem in $\mathbb{R}^n,$ $n\geq 1,$ for a semilinear
damped wave equation with nonlinear memory. Global existence and asymptotic
behavior as $t\rightarrow\infty$ of small data solutions have been established
in the case when $1\leq n\leq3.$ Moreover, we derive a blow-up result under
some positive data in any dimensional space.

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