An Asymptotic Analysis of the Damped Wave Equation
Julian L. Davis, Edward L. Reiss · Transactions of the Society of Rheology · 1970
We consider a mixed boundary initial value problem for the one-dimensional damped wave equation εvtt+vt−vxx=0. At x=0,1, v is assumed to vanish. Here ε>0 is a parameter which is small when the damping is large. Boundary layer and ray methods are employed to study the solution of this problem. For “quiescent” initial data, the motion is diffusive with diffusion occurring with two time scales. For “oscillatory” initial data, strongly damped, rapidly oscillating waves occur. The problem is a generalization of the damped linear oscillator.