Laplace asymptotics for generalized K.P.P. equation

Rouquès, Jean-Philippe. "Laplace asymptotics for generalized K.P.P. equation." ESAIM: Probability and Statistics 1 (2010): 225-258. <http://eudml.org/doc/197741>.

@article{Rouquès2010,
abstract = { Consider a one dimensional nonlinear reaction-diffusion equation (KPP equation) with non-homogeneous second order term, discontinuous initial condition and small parameter. For points ahead of the Freidlin-KPP front, the solution tends to 0 and we obtain sharp asymptotics (i.e. non logarithmic). Our study follows the work of Ben Arous and Rouault who solved this problem in the homogeneous case. Our proof is probabilistic, and is based on the Feynman-Kac formula and the large deviation principle satisfied by the related diffusions. We use the Laplace method on Wiener space. The main difficulties come from the nonlinearity and the possibility for the endpoint of the optimal path to lie on the boundary of the support of the initial condition. },
author = {Rouquès, Jean-Philippe},
journal = {ESAIM: Probability and Statistics},
keywords = {Generalized KPP equation / Feynman-Kac formula / diffusion / large deviations / Laplace method / stochastic Taylor expansion / Skorokhod integral.; nonlinear diffusion; probabilistic formulation; Feynman-Kac formula},
language = {eng},
month = {3},
pages = {225-258},
publisher = {EDP Sciences},
title = {Laplace asymptotics for generalized K.P.P. equation},
url = {http://eudml.org/doc/197741},
volume = {1},
year = {2010},
}

TY - JOUR
AU - Rouquès, Jean-Philippe
TI - Laplace asymptotics for generalized K.P.P. equation
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 1
SP - 225
EP - 258
AB - Consider a one dimensional nonlinear reaction-diffusion equation (KPP equation) with non-homogeneous second order term, discontinuous initial condition and small parameter. For points ahead of the Freidlin-KPP front, the solution tends to 0 and we obtain sharp asymptotics (i.e. non logarithmic). Our study follows the work of Ben Arous and Rouault who solved this problem in the homogeneous case. Our proof is probabilistic, and is based on the Feynman-Kac formula and the large deviation principle satisfied by the related diffusions. We use the Laplace method on Wiener space. The main difficulties come from the nonlinearity and the possibility for the endpoint of the optimal path to lie on the boundary of the support of the initial condition.
LA - eng
KW - Generalized KPP equation / Feynman-Kac formula / diffusion / large deviations / Laplace method / stochastic Taylor expansion / Skorokhod integral.; nonlinear diffusion; probabilistic formulation; Feynman-Kac formula
UR - http://eudml.org/doc/197741
ER -