TY - JOUR
T1 - On the explosion problem in a ball
AU - Novikov, Alexei
N1 - Publisher Copyright:
© 2015 International Press.
PY - 2015
Y1 - 2015
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.
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U2 - 10.4310/CMS.2015.v13.n4.a9
DO - 10.4310/CMS.2015.v13.n4.a9
M3 - Article
AN - SCOPUS:84930031778
SN - 1539-6746
VL - 13
SP - 1025
EP - 1032
JO - Communications in Mathematical Sciences
JF - Communications in Mathematical Sciences
IS - 4
ER -