Electron. J. Diff. Equ., Vol. 2015 (2015), No. 162, pp. 1-14.

Estimates for damped fractional wave equations and applications

Jiecheng Chen, Dashan Fan, Chunjie Zhang

Abstract:
In our previous article [1] we estimated the $L^p$-norm ($p\geq 1$) of the solution to damped fractional wave equation. In this article, we prove other $L^p$ estimates, with some emphasis on requiring less regularity of the initial data. We also study the Strichartz type estimate of this equation. Finally we present some application of these estimates, for proving existence of global solutions to semilinear damped fractional wave equations.

Submitted November 30, 2014. Published June 16, 2015.
Math Subject Classifications: 35L05, 46E35, 42B37.
Key Words: Damped fractional wave equation; $L^p$-estimate; Strichartz estimate.

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Jiecheng Chen
Department of Mathematics
Zhejiang Normal University
Jinhua 321004, China
email: jcchen@zjnu.edu.cn
Dashan Fan
Department of Mathematics
University of Wisconsin
Milwaukee, WI 53201, USA
email: fan@uwm.edu
Chunjie Zhang
Department of Mathematics
Hangzhou Dianzi University
Hangzhou 310018, China
email: purezhang@hdu.edu.cn

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