Study Of Blow-up Of Solutions To A Class Of Fourth-order Semilinear Parabolic Equations

In this paper,we study the upper and lower bounds for the blow-up time to the following fourth-order semilinear parabolic equationAt first,we prove that the solution must blow up in finite time if the initial energy satisfies one of the following conditions:Subsequently,we also prove that the solution blows up in finite time for arbitrary posi-tive initial energy.At last,by constructing a new control functional and applying the Sobolev embed-ding theorem,we obtain an estimate of lower bound of blow-up time to the solution.In the thesis,we only assume that k(t)is a monotone function without assuming that k(t)/k(t)is uniformly bounded.The condition given in this paper is weaker than that in Philip*-pine’s article Blow-up phenomena for a class of fourth-order parabolic problems published in Proc.AmerMath.Soc..