The explosion problem in a flow

Details The explosion problem in a flow The explosion problem in a flow

2009-07-29

arxiv.org/abs/0907.5230v1

Mathematics

Analysis of PDEs

28 pages, Latex, numbysec.sty style, 2 figures (.eps and .ps)

Scientific paper

We consider the explosion problem in an incompressible flow introduced in the paper of H. Berestycki, L. Kagan, G. Joulin and G. Sivashinsky. We use a novel $L^p-L^\infty$ estimate for elliptic advection-diffusion problems to show that the explosion threshold obeys a positive lower bound which is uniform in the advecting flow. We also identify the flows for which the explosion threshold tends to infinity as their amplitude grows and obtain an effective description of the explosion threshold in the strong flow asymptotics in a two-dimensional one-cell flow.

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