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Article Contents

# Initial boundary value problem for the singularly perturbed Boussinesq-type equation

• 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.
Mathematics Subject Classification: Primary: 35A01, 35L35; Secondary: 35G31, 35Q35.

 Citation:

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