Boundary control of viscosity Degasperis–Procesi equation

This paper investigates the boundary control problem of the viscosity Degasperis–Procesi equation in [0, 1]. Results of the existence of a solution to the viscosity Degasperis–Procesi equation in a short time interval under the boundary condition, are given in the paper. It proves the global exponential stability under the given boundary condition in L2L2, H1H1, H2H2, H3H3 space.