We study the asymptotics of Allen–Cahn-type bistable reaction-diffusion equations which are additively perturbed by a stochastic forcing (time white noise). The conclusion is that the long time, large space behavior of the solutions is governed by an interface moving with curvature dependent normal velocity which is additively perturbed by time white noise. The result is global in time and does not require any regularity assumptions on the evolving front. The main tools are (i) the notion of stochastic (pathwise) solution for nonlinear degenerate parabolic equations with multiplicative rough (stochastic) time dependence, which has been developed by the authors, and (ii) the theory of generalized front propagation put forward by the second author and collaborators to establish the onset of moving fronts in the asymptotics of reaction-diffusion equations.

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Pierre-Louis Lions ^{1};
Panagiotis E. Souganidis ^{2}

@article{CRMATH_2020__358_8_931_0, author = {Pierre-Louis Lions and Panagiotis E. Souganidis}, title = {The asymptotics of stochastically perturbed reaction-diffusion equations and front propagation}, journal = {Comptes Rendus. Math\'ematique}, pages = {931--938}, publisher = {Acad\'emie des sciences, Paris}, volume = {358}, number = {8}, year = {2020}, doi = {10.5802/crmath.117}, language = {en}, }

TY - JOUR AU - Pierre-Louis Lions AU - Panagiotis E. Souganidis TI - The asymptotics of stochastically perturbed reaction-diffusion equations and front propagation JO - Comptes Rendus. Mathématique PY - 2020 SP - 931 EP - 938 VL - 358 IS - 8 PB - Académie des sciences, Paris DO - 10.5802/crmath.117 LA - en ID - CRMATH_2020__358_8_931_0 ER -

%0 Journal Article %A Pierre-Louis Lions %A Panagiotis E. Souganidis %T The asymptotics of stochastically perturbed reaction-diffusion equations and front propagation %J Comptes Rendus. Mathématique %D 2020 %P 931-938 %V 358 %N 8 %I Académie des sciences, Paris %R 10.5802/crmath.117 %G en %F CRMATH_2020__358_8_931_0

Pierre-Louis Lions; Panagiotis E. Souganidis. The asymptotics of stochastically perturbed reaction-diffusion equations and front propagation. Comptes Rendus. Mathématique, Volume 358 (2020) no. 8, pp. 931-938. doi : 10.5802/crmath.117. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.117/

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