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In this paper, the existence and the uniqueness of the global generalized solution and the global classical solution for the initial boundary value problem of the generalized cubic double dispersion equation are proved. The nonexistence of global solution for the initial boundary value problem of the generalized cubic double dispersion equation is discussed.

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In this paper we study the existence and uniqueness of the global generalized solution and the global classical solution, the blowup of the solution and the energy decay of the solutions of the initial-boundary value problems for a class of nonlinear wave equations.

SUMMARYThe existence and uniqueness of the global generalized solution and the global classical solution to the initial boundary value problem for a system of generalized IMBq equationsare proved. This paper also arrives at some su cient conditions of blow up of the solution in ÿnite time.