### Abstract

In Ω⊂R^{n} 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 L^{p}-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 language | English (US) |
---|---|

Pages (from-to) | 1025-1032 |

Number of pages | 8 |

Journal | Communications in Mathematical Sciences |

Volume | 13 |

Issue number | 4 |

DOIs | |

State | Published - Jan 1 2015 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

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*Communications in Mathematical Sciences*, vol. 13, no. 4, pp. 1025-1032. https://doi.org/10.4310/CMS.2015.v13.n4.a9

**On the explosion problem in a ball.** / Novikov, Alexei.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On the explosion problem in a ball

AU - Novikov, Alexei

PY - 2015/1/1

Y1 - 2015/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84930031778&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84930031778&partnerID=8YFLogxK

U2 - 10.4310/CMS.2015.v13.n4.a9

DO - 10.4310/CMS.2015.v13.n4.a9

M3 - Article

VL - 13

SP - 1025

EP - 1032

JO - Communications in Mathematical Sciences

JF - Communications in Mathematical Sciences

SN - 1539-6746

IS - 4

ER -