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arXiv · 1602.03339

Attractors for the strongly damped wave equation with $p$-Laplacian

Azer Khanmamedov·Zehra Şen
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Abstract

This paper is concerned with the initial boundary value problem for one dimensional strongly damped wave equation involving $p$-Laplacian. For $p>2$, we establish the existence of weak local attractors for this problem in $W_{0}^{1,p}(0,1)\times L^{2}(0,1)$. Under restriction $2<p<4$, we prove that the semigroup, generated by the considered problem, possesses a strong global attractor in $W_{0}^{1,p}(0,1)\times L^{2}(0,1)$ and this attractor is a bounded subset of $W^{1,\infty }(0,1)\times W^{1,\infty }(0,1)$.

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Azer Khanmamedov, Zehra Şen. 2016-06-13. Attractors for the strongly damped wave equation with $p$-Laplacian. https://doi.org/10.1002/mma.4315

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