On the Solution of Reduced Wave Equation with Damping - Misir, Adil (Communications in Mathematics and Applications, 2010)
In this paper we find particular solutions of Reduced wave equation with damping in the form $Δ u+k^{2}n( x) u+μ \vert abla u\vert =0$, $\mathbb{R}^{n}$, $μ\in\mathbb{R} $ and $n(x)$ is a continuous function on $Ω$, 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.
Keywords: Helmholtz equation; Reduced wave equation; Differential equation