Universal Bounds for Global Solutions of Fast Diffusion Equations with Source

Abstract

We prove a universal bound, independent of initial data, for all global nonnegative solutions of fast diffusion equations of the form , with zero Dirichlet boundary conditions. Up to now, such results were only available in the semilinear and slow diffusion cases m≥ 1.

Keywords:

• Nonlinear degenerate parabolic equations
• Fast diffusion
• Global solutions
• A priori estimates
• Universal bounds
• AMS Subject Classification:35K60
• 35K65
• 35B45