On a class of degenerate parabolic equations with dynamic boundary conditions

Details On a class of degenerate parabolic equations with dynamic boundary conditions On a class of degenerate parabolic equations with dynamic boundary conditions

2011-09-02

arxiv.org/abs/1109.0469v5

Mathematics

Dynamical Systems

to appear in JDE

Scientific paper

We consider a quasi-linear parabolic equation with nonlinear dynamic boundary conditions occurring as a natural generalization of the semilinear reaction-diffusion equation with dynamic boundary conditions. The corresponding class of initial and boundary value problems has already been studied previously, proving well-posedness and the existence of the global attractor. The goal of this note is to show that the previous analysis can be redone for more general nonlinearities by proving an additional (uniform) L\infty-estimate on the solutions. In particular, we derive new conditions which reflect an exact balance between the two nonlinear mechanisms involved, even when both the nonlinear (source) terms contribute in opposite directions.

Affiliated with

Also associated with

No associations

Rating

On a class of degenerate parabolic equations with dynamic boundary conditions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On a class of degenerate parabolic equations with dynamic boundary conditions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On a class of degenerate parabolic equations with dynamic boundary conditions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-688102