Universal bounds for global solutions of a forced porous medium equation

  • Winkler M
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Abstract

We show that in a smooth bounded domain Ω ⊂ ℝn, n ≥ 2, all global nonnegative solutions of ut- Δum= upwith zero boundary data are uniformly bounded in Ω × (τ,∞) by a constant depending on Ω, p; and τ but not on u0, provided that 1 < m < p < [(n + 1)/(n - 1)]m. Furthermore, we prove an a priori bound in L∞(Ω × (0,∞)) depending on ||u0||L∞(Ω)under the optimal condition 1 < m < p < [(n + 2)/(n - 2)]m. © 2004 Elsevier Ltd. All rights reserved.

Author-supplied keywords

  • A priori estimates
  • Nonlinear diffusion

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Authors

  • Michael Winkler

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