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Abstract: The existence and uniqueness of the local generalized solution to the initial boundary value problem for the three-dimensional damped nonlinear hyperbolic equation are proved. The paper arrives at some sufficient conditions for blow up of the solutions in finite time by two methods. An example is given. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

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 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 global existence of solutions to the initial boundary value problem for a class of quasi-linear wave equations with viscous damping and source terms is studied by using a combination of Galerkin approximations, compactness, and monotonicity methods. [Copyright &y& Elsevier]