BLOWUP FOR SEMILINEAR PARABOLIC EQUATION WITH LOGARITHMIC NONLINEARITY

In this paper, we proposed a new method to prove the blowup at +infinity for the solution of the initial boundary value problem for a class of semilinear parabolic equations with logarithmic nonlinearity at sub-critical initial energy level by contradiction. Moreover, following the idea of contradiction, we obtained a sufficient criterion for the blowup at +infinity of the solution with arbitrarily positive initial energy by defining a new auxiliary function, in which the location of the initial data concerning the unstable set is not required.