Exact solution to a multidimensional wave equation with delay

Abstract This paper deals with a mixed problem for the wave equation with discrete delay τ > 0 , u t t ( t , x ) = a 1 2 Δ x u ( t , x ) + a 2 2 Δ x u ( t − τ , x ) + b 1 u ( t , x ) + b 2 u ( t − τ , x ) , t > τ , 0 ≤ x ≤ l , with Dirichlet boundary conditions. The exact infinite series solution is constructed by the method of separation of variables, where the time-dependent functions of the decomposition satisfy second-order delay differential equations. Our approach is based on and extends the work by Rodriguez, Roales and Martin (Applied Mathematics and Computation, 2012).