BLOW-UP OF WEAK SOLUTIONS FOR A HIGHER-ORDER HEAT EQUATION WITH LOGARITHMIC NONLINEARITY

This paper deal with the initial boundary value problem for a higher-order heat equation with logarithmic source term ut + (-& UDelta;)mu -& UDelta;ut = uk-2u ln |u|. We obtain blow-up of weak solutions in the finite time, by employing potential well technique and concave technique. In addition, the upper bound of blow-up time is considered. This improves and extends some previous studies.