On the Solution of Reduced Wave Equation with Damping

Abstract

In this paper we find particular solutions of Reduced wave equation with damping in the form $\Delta u+k^{2}n( \mathbf{x}) u+\mu \vert \nabla u\vert =0$, $\mathbb{R}^{n}$, $\mu\in\mathbb{R} $ and $n(\mathbf{x)}$ is a continuous function on $\Omega$, by making use of Fundamental solution $u=\frac{\exp(ikR)}{R}$ of the scalar Helmholtz equation and employing a variation of constant technique. Moreover, some examples are given to illustrate the importance of our results.