Asymptotic profile of solutions to the linearized double dispersion equation on the half space $\mathbb{R}^{n}_{+}$

Yu-Zhu Wang; Si Chen; Menglong Su

doi:10.3934/eect.2017032

Article Contents

2017, Volume 6, Issue 4: 629-645. Doi: 10.3934/eect.2017032

This issue Previous Article Degeneracy in finite time of 1D quasilinear wave equations Ⅱ Next Article

Asymptotic profile of solutions to the linearized double dispersion equation on the half space $\mathbb{R}^{n}_{+}$

1.
School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450011, China
2.
School of Sciences, Zhejiang Tongji Vocational College of Science and Technology, Hangzhou 310001, China
3.
School of Mathematics, Luoyang Normal University, Luoyang 471934, China

* Corresponding author: Yu-Zhu Wang
* Corresponding author: Yu-Zhu Wang

Received: April 30, 2017

Revised: June 30, 2017

Published: November 2017

The first author is supported by Innovation Scientists and Technicians Troop Construction Projects of Henan Province(Grant No.14HASTIT041) and the third author is supported by National Natural Science Foundation of China(Grant No. 11671188).

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Abstract

In this paper, we investigate the initial boundary value problem for the linearized double dispersion equation on the half space $\mathbb{R}^{n}_{+}$. We convert the initial boundary value problem into the initial value problem by odd reflection. The asymptotic profile of solutions to the initial boundary value problem is derived by establishing the asymptotic profile of solutions to the initial value problem. More precisely, the asymptotic profile of solutions is associated with the convolution of the partial derivative of the fundamental solutions of heat equation and the fundamental solutions of free wave equation.

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Mathematics Subject Classification: Primary: 35B40; Secondary: 35L35.

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