Serrin, "Global existence and global nonexistence of solutions of the Cauchy problem for a nonlinearly damped wave
equation," Journal of Mathematical Analysis and Applications, vol.
Toward this goal, a damped wave equation with a spatial dependent damping parameter is presented, where a parameter variation allows controlling the absorption and therefore minimizes those undesirable reflections.
This paper is organized as follows: some basic notions about the PSTD method and a theoretical analysis of the damped wave equation are presented, paying special attention to those cases with a spatially varying damping coefficient.
In this section, the formulation of the PSTD damped wave equation is presented and the properties of an incrementally progressive damping medium are studied.
Among the topics are some spectral properties of rooms and passages domains and their skeletons, asymptotic parabolicity for strongly damped wave
equations, a minimal uncertainty product for one-dimensional semi-classical wave packets, one-dimensional Schrodinger operations with local point interactions, and proscribed asymptotic behavior for nonlinear second-order dynamic equations.
O.Ahmad, Fourth Order Compact Method for one dimensional homogeneous Damped Wave
Equation, PJS, Vol.
Such situations are frequently met when dealing with waves whose behavior exhibits diffusion phenomena which can only be described using the damped wave equation.
A damped wave in general is a wave whose amplitude of oscillation decreases with time.
In fact, many authors have studied different classes of damped wave equations by investigating their solutions or by studying their asymptotic behavior [17-19].
Finite Difference Method (FDM) and Fourth Order Compact Method (FOCM) are presented in this paper for the solutions of the well known one dimensional Homogeneous Damped Wave Equation.
Key words: Finite Difference Method, Fourth Order Compact Method, Damped Wave Equation.
Consider the second order one dimensional homogenous damped wave equation