TY - JOUR
T1 - Traveling wave solutions of advection-diffusion equations with nonlinear diffusion
AU - Monsaingeon, L.
AU - Novikov, A.
AU - Roquejoffre, J. M.
N1 - Funding Information:
L.M. would like to thank the PREFERRED French ANR project and NSF grant DMS-0908011 for financial support, Penn State University and Stanford University for their hospitality. A.N. was supported by the NSF grant DMS-0908011.
PY - 2013
Y1 - 2013
N2 - We study the existence of particular traveling wave solutions of a nonlinear parabolic degenerate diffusion equation with a shear flow. Under some assumptions we prove that such solutions exist at least for propagation speeds cε]C*,+∞[, where C*>0 is explicitly computed but may not be optimal. We also prove that a free boundary hypersurface separates a region where u=0 and a region where u>0, and that this free boundary can be globally parametrized as a Lipschitz continuous graph under some additional non-degeneracy hypothesis; we investigate solutions which are, in the region u>0, planar and linear at infinity in the propagation direction, with slope equal to the propagation speed.
AB - We study the existence of particular traveling wave solutions of a nonlinear parabolic degenerate diffusion equation with a shear flow. Under some assumptions we prove that such solutions exist at least for propagation speeds cε]C*,+∞[, where C*>0 is explicitly computed but may not be optimal. We also prove that a free boundary hypersurface separates a region where u=0 and a region where u>0, and that this free boundary can be globally parametrized as a Lipschitz continuous graph under some additional non-degeneracy hypothesis; we investigate solutions which are, in the region u>0, planar and linear at infinity in the propagation direction, with slope equal to the propagation speed.
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U2 - 10.1016/j.anihpc.2012.11.003
DO - 10.1016/j.anihpc.2012.11.003
M3 - Article
AN - SCOPUS:84881181798
SN - 0294-1449
VL - 30
SP - 705
EP - 735
JO - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
JF - Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
IS - 4
ER -