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Nonexistence of global solutions to the initial boundary value problem for the singularly perturbed sixth-order Boussinesq-type equation. (English) Zbl 1442.76028

Summary: We are concerned with the singularly perturbed Boussinesq-type equation including the singularly perturbed sixth-order Boussinesq equation, which describes the bidirectional 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 nonexistence of global solution to the initial boundary value problem for the singularly perturbed Boussinesq-type equation is discussed and two examples are given.

MSC:

76B25 Solitary waves for incompressible inviscid fluids
35B25 Singular perturbations in context of PDEs
35Q53 KdV equations (Korteweg-de Vries equations)
76B45 Capillarity (surface tension) for incompressible inviscid fluids
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References:

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