Derivative blow-up and beyond for quasilinear parabolic equations
Марек Фила, Gary M. Lieberman · Differential and Integral Equations · 1994
L 00 -blow-up of solutions of semilinear parabolic equations has received considerable interest.Several major problems like sufficient conditions for blow-up, the form of the blow-up set, the profile of the solution near a blow-up point or the existence after the blow-up time have been studied.The aim of this paper is to deal with similar questions for a related phenomenon, namely blow-up of the spatial derivative while the solution itself stays bounded.We proceed via the maximum and comparison principles.