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arXiv · 1607.01839

Asymptotic profiles of solutions for structural damped wave equations

Ryo Ikehata·Hiroshi Takeda
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Abstract

In this paper, we obtain several asymptotic profiles of solutions to the Cauchy problem for structurally damped wave equations $\partial_{t}^{2} u - \Delta u + \nu (-\Delta)^{\sigma} \partial_{t} u=0$, where $\nu >0$ and $0< \sigma \le1$. Our result is the approximation formula of the solution by a constant multiple of a special function as $t \to \infty$, which states that the asymptotic profiles of the solutions are classified into $5$ patterns depending on the values $\nu$ and $\sigma$.

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Ryo Ikehata, Hiroshi Takeda. 2016-07-06. Asymptotic profiles of solutions for structural damped wave equations. https://arxiv.org/abs/1607.01839

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