Analytical treatment and convergence of the Adomian decomposition method for a system of coupled damped wave equations

An abstract result is proved for the convergence of Adomian decomposition method for partial differential equations that model evolutionary systems. Moreover, we prove that this decomposition scheme applied to a system of wave equations coupled in parallel with homogeneous Dirichlet boundary conditions, is convergent in a suitable Hilbert space. Furthermore, this technique is utilized to find closed-form solutions for the problem under consideration.