Document Type : Research Paper
Author
Instituto de Investigacion ,FCM-UNMSM, Av. Venezuela S/N, Lima- Peru.
Abstract
The current paper discusses the global existence and asymptotic behavior of solutions of the following new nonlocal problem
$$ u_{tt}- M\left(\displaystyle \int_{\Omega}|\nabla u|^{2}\, dx\right)\triangle u + \delta u_{t}= |u|^{\rho-2}u \log|u|, \quad \text{in}\ \Omega \times ]0,\infty[, $$
where
\begin{equation*}
M(s)=\left\{\begin{array}{ll}
{a-bs,}&{\text{for}\ s \in [0,\frac{a}{b}[,}\\
{0,}&{\text{for}\ s \in [\frac{a}{b}, +\infty[.}
\end{array}
\right.
\end{equation*}
If the initial data are appropriately small, we derive existence of global strong solutions and the exponential decay of the energy.
Keywords
Main Subjects
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