Blow Up Phenomena For Two Classes Fourth-Order Nonlinear Evolution Equations

The thesis consider two classes of fourth order nonlinear evolution partial differential equation with the initial-boundary value problem.In he first part,by using the eigenfunctions for a specific eigenvalue problem,Jensen inequality etc,we construct some ordinary differential inequalities with respect to time for two classes of fourth order nonlinear equation.Then,we prove that the solutions of the problem will blow-up in finite time.Furthermore,we not only present some sufficient conditions on nonlinear functions under which the solutions will blow up in finite time but also establish the time upper bound of blow up time.In the second part,by using the energy method,we establish several ordinary differential inequalities with respect to time,then we proved that the solutions of two classes fourth order equation with initial boundary value conditions will occur blow up phenomena in finite time.Some sufficient conditions added to nonlinear functions and the initial data under which the solutions of the problems will blow up,are also given.Several examples are also given after the theorems.