Nonexistence of Global Solutions to the Initial Boundary Value Problem for the Singularly Perturbed Sixth-Order Boussinesq-Type Equation

We are concerned with the singularly perturbed Boussinesq-type equation including the singularly perturbed sixth-order Boussinesq equation, which Hockey Puck describes the bidirectional propagation of small amplitude and long capillary-gravity waves on the surface of shallow water for Body Wash bond number (surface tension parameter) less than but very close to 1/3.The nonexistence of global solution to the initial boundary value problem for the singularly perturbed Boussinesq-type equation is discussed and two examples are given.