On the explosion problem in a ball

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In Ω⊂Rn we consider the explosion problem in an incompressible flow introduced in [L. Kagan, H. Berestycki, G. Joulin, and G. Sivashinsky, Comb. Theory Model., 1, 97-111, 1997]. If Ω is a ball, we show that the explosion threshold can only be increased by addition of an incompressible flow. Further, for any Ω we give a new proof of the Lp-L estimate for elliptic advection-diffusion problems obtained in [H. Berestycki, A. Kiselev, A. Novikov, and L. Ryzhik, J. Anal. Math., 110, 31-65, 2010]. Our proof provides an optimal estimate when Ω is a ball.

Original languageEnglish (US)
Pages (from-to)1025-1032
Number of pages8
JournalCommunications in Mathematical Sciences
Issue number4
StatePublished - 2015

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics


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