Israel Journal of Mathematics

, 98:141

Critical exponent and critical blow-up for quasilinear parabolic equations



We consider nonnegative solutions to the Cauchy problem or to the exterior Dirichlet problem for the quasilinear parabolic equationsutum+up with 1<m<p. In case of the Cauchy problem, it is well known thatpm*=m+2/N is the critical exponent of blow-up. Namely, ifp<pm*, then all nontrivial solutions blow up in finite time (blow-up case), and ifp>pm*, then there are nontrivial global solutions (global existence case). In this paper we show: (i) For the Cauchy problem,pm* belongs to the blow-up case. (ii) For the exterior Dirichlet problem,pm* also gives the critical exponent of blow-up.


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© Hebrew University 1997

Authors and Affiliations

  1. 1.Department of MathematicsTokyo Metropolitan UniversityTokyoJapan
  2. 2.Department of MathematicsTokyo Metropolitan College of Aeronautical EngineeringTokyoJapan
  3. 3.Department of Mathematics, Faculty of ArtsKokushikan UniversityTokyoJapan

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