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Initial boundary value problem of the generalized cubic double dispersion equation. (English) Zbl 1066.35087

Existence and uniqueness of the global generalized solution and the global classical solution to the initial boundary value problem of the generalized cubic double dispersion equation are proved. The authors also give sufficient conditions for the nonexistence of the global solution to the same problem. As applications of their results, they can prove that the above problem has a unique global generalized solution, while the problem of the double dispersion equation does not possess global generalized and classical solutions under certain assumptions.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35G25 Initial value problems for nonlinear higher-order PDEs
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