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Abstract: In this paper, the asymptotic behavior of the solution to the initial–boundary value problem for a nonlinear evolution equation of fourth order is studied. The sufficient conditions for blow-up of the solutions to the initial–boundary value problems for Eq. (1) are given. [Copyright &y& Elsevier]

Abstract: In the note, we study the existence and uniqueness of the global generalized solution for the following initial boundary value problem: where is a bounded domain in with smooth boundary denotes the Laplacian operator in , denotes the gradient operator and is a given nonlinear function. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

This paper gives the sufficient conditions of blow-up of the solution of a nonlinear damped hyperbolic equation with the initial boundary value conditions in finite time and proves the existence and uniqueness of the local generalized solution of this problem. [Copyright &y& Elsevier]

In this paper, the existence and the uniqueness of the global strong solution and the global classical solution for the Cauchy problem of the multidimensional generalized IMBq equation are proved. The nonexistence of the global solution for the Cauchy problem of the generalized IMBq equation is discussed. [Copyright &y& Elsevier]