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The Quenching Problem on the N-dimensional Ball

  • Marek Fila
  • Josephus Hulshof
  • Pavol Quittner
Chapter
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 7)

Abstract

Consider the problem where β > 0 and Ω = B R (0) ≔ x ∈ IR N ; |x| < R. It is known ([AW]) that there is a positive number R o = R o (N,β) such that u exists globally if R < R o while for R> R o the solution u reaches zero in a finite time T (it quenches). The only point x o for which u(x o , t) → 0 as t 2192 T is x o = 0 (see [AK]).

Keywords

Maximum Principle Finite Time Singular Solution Positive Equilibrium Infinite Time 
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Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Marek Fila
    • 1
  • Josephus Hulshof
    • 2
  • Pavol Quittner
    • 3
  1. 1.Dept. of Math. AnalysisComenius Univ.BratislavaCzechoslovakia
  2. 2.Mathematical Inst.Leiden Univ.LeidenThe Netherlands
  3. 3.Inst. of Appl. Math.Comenius Univ.BratislavaCzechoslovakia

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