Analytical solution of a hyperbolic partial differential equation and its application

Purpose The purpose of this paper is to investigate the analytical solution of a hyperbolic partial differential equation (PDE) and its application. Design/methodology/approach The change of variables and the method of successive approximations are introduced. The Volterra transformation and boundary control scheme are adopted in the analysis of the reaction-diffusion system. Findings A detailed and complete calculation process of the analytical solution of hyperbolic PDE (1)-(3) is given. Based on the Volterra transformation, a reaction-diffusion system is controlled by boundary control. Originality/value The introduced approach is interesting for the solution of hyperbolic PDE and boundary control of the reaction-diffusion system.