Representation of Classical Solutions to a Linear Wave Equation with Pure Delay

Abstract

For a wave equation with pure delay, we study an inhomogeneous initial-boundary value problem in a bounded 1D domain. Under smoothness assumptions, we prove unique existence of classical solutions for any given finite time horizon and give their explicit representation. Continuous dependence on the data in a weak extrapolated norm is also shown.

11 pages, 1 figure

References in corpus (1)

• On Classical Solvability for a Linear 1D Heat Equation with Constant Delay