$L^p$ - $L^q$ estimates for damped wave equations with odd initial data

Abstract

We study the Cauchy problem for the damped wave equation. In a previous paper [16] the author has shown the $L^p$ - $L^q$ estimates between the solutions of the damped wave equation and the solutions of the corresponding heat equation. In this paper, we show new $L^p$ - $L^q$ estimates for the damped wave equation with odd initial data.

Keywords

• Damped wave equation
• $L^p$ - $L^q$ estimate
• odd initial data.