Analysis and numerical solution of Benjamin-Bona-Mahony equation with moving boundary

Keywords: Benjamin–Bona–Mahony equation Method of compactness Moving boundary Crank–Nicolson method a b s t r a c t In this work we present the existence, the uniqueness and numerical solutions for a mathematical model associated with equations of Benjamin–Bona–Mahony type in a domain with moving boundary. We apply the Galerkin method, multiplier techniques, energy estimates and compactness results to obtain the existence and uniqueness. For numerical solutions , we shall employ the finite element method together with the Crank–Nicolson method. Some numerical experiments are presented to show the moving boundary for the problem.