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

[摘要] We are concerned with the singularly perturbed Boussinesq-type equation includingthe singularly perturbed sixth-order Boussinesq equation, which describes the bidirectionalpropagation of small amplitude and long capillary-gravity waves on the surface of shallow waterfor bond number (surface tension parameter) less than but very close to 1/3. The nonexistenceof global solution to the initial boundary value problem for the singularly perturbed Boussinesq-typeequation is discussed and two examples are given.

[学科分类] 应用数学