Display Abstract
 Title Global existence of the singularly perturbed Boussinesq-type equation
 Name ChangMing Song Country Peoples Rep of China Email cmsongh@163.com Co-Author(s) Submit Time 2014-02-19 03:12:44 Session Special Session 37: Global or/and blowup solutions for nonlinear evolution equations and their applications
 Contents We are concerned with the singularly perturbed Boussinesq-type equation including the singularly perturbed sixth-order Boussinesq equation, which describes the bi-directional propagation of small amplitude and long capillary-gravity waves on the surface of shallow water for bond number (surface tension parameter) less than but very close to $1/3$. The existence and uniqueness of the global generalized solution and the global classical solution of the initial boundary value problem for the singularly perturbed Boussinesq-type equation are proved. The nonexistence of global solution of the above-problem is discussed and two examples are given