Matzoh ball soup revisited: The boundary regularity issue

Rolando Magnanini, Shigeru Sakaguchi

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)

Abstract

We consider nonlinear diffusion equations of the form ∂tu = Δφ(u) in RN with N ≥ 2. When φ(s) ≡ s, this is just the heat equation. Let Ω be a domain in RN, where ∂Ω is bounded and ∂Ω=∂RNΩ̄. We consider the initial-boundary value problem, where the initial value equals zero and the boundary value equals 1, and the Cauchy problem where the initial data is the characteristic function of the set Ωc=RNΩ. We settle the boundary regularity issue for the characterization of the sphere as a stationary level surface of the solution u:, no regularity assumption is needed for ∂Ω.

Original languageEnglish
Pages (from-to)2023-2032
Number of pages10
JournalMathematical Methods in the Applied Sciences
Volume36
Issue number15
DOIs
Publication statusPublished - 2013 Oct

Keywords

  • Cauchy problem
  • heat equation
  • initial behavior
  • initial-boundary value problem
  • nonlinear diffusion
  • sphere
  • stationary level surface

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

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