Critical exponent for damped wave equations with nonlinear memory

Ahmad Fino

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arXiv · 1004.3850

Critical exponent for damped wave equations with nonlinear memory

Ahmad Fino

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Abstract

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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Ahmad Fino. 2010-09-07. Critical exponent for damped wave equations with nonlinear memory. https://arxiv.org/abs/1004.3850

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