Abstract: In this paper, the initial boundary value problems of the nonlinear Sobolev-Galpern equation are studied. The existence, uniqueness of local solution for the problem are obtained by means of a special Green’s function and the contraction mapping principle. Finally, the blow-up of solution in finite time under some assumed conditions is proved with the aid of Jensen’s inequality.

Key words: nonlinear Sobolev-Galpern equations, Green’s function, blow-up, Jensen’s inequality