Infinite time blow-up of solutions to a nonlinear parabolic problem

[摘要] 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 the L-infinity-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 the L-infinity-norm. (C) 1997 Academic Press.

[发布日期] 1997-09-20