Infinite Time Blow-Up of Solutions to a Nonlinear Parabolic Problem

We investigate the blow-up of solutions of nonuniformly parabolic equations. It will be shown that the gradient of the solution tends to infinity as time goes to infinity, even though theL∞-norm of the solution may remain uniformly bounded. This phenomenon is in contrast with a result for semilinear heat equations, where it follows from regularity theory that the solution converges to an equilibrium if it is uniformly bounded in theL∞-norm.