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In this paper, we prove that the Cauchy problem for the following damped generalized IMBq equation, utt-uxx-uxxtt+ν2uxxt=f(u)xx,x∈R,t>0, admits a unique global generalized solution in C3([0,∞);Wm,p(R)∩L∞(R)∩L2(R))(1≤p≤∞,m≥0) and a unique global classical solution in C3([0,∞);Wm,p(R)∩L∞(R)∩L2(R))(m>2+1p). Moreover, the blow up of the solution for the Cauchy problem of damped generalized IMBq equation is studied. We also prove that the Cauchy problem of the above-mentioned equation has a unique global generalized solution in C2([0,∞);Hs(R))(s>12) and a unique global classical solution in C2([0,∞);Hs(R))(s>52), and discuss the blow up of the solution. [ABSTRACT FROM AUTHOR]

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 existence and uniqueness of the local generalized solution and the local classical solution for the initial boundary value problem of the quasi-linear wave equation with viscous damping are proved. The nonexistence of the global solution for this problem is discussed by an ordinary differential inequality. Finally, an example is given. [Copyright &y& Elsevier]