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

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.

Show me the PDF file (263 KB), TEX file, and other files for this article.

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

Return to the EJDE web page