Geodesic
Stochastic model of the Cauchy--Robin problem for systems of nonlinear parabolic equations
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 33, Tome 515 (2022), pp. 39-71

Voir la notice de l'article provenant de la source Math-Net.Ru

We derive stochastic equations to describe reflected diffusion processes associated with the Cauchy–Neumann problem for systems of nonlinear parabolic equations in non-divergent form. The construction of a solution to the arized stochastic problem is based on a localization procedure that allows to reduce the problem in a closed domain to the corresponding problem in the half space. As a result we obtain a probabilistic representation of a weak solution to the Cauchy–Neumann problem in a bounded domain with a smooth boundary. 
@article{ZNSL_2022_515_a3,
     author = {Ya. I. Belopolskaya},
     title = {Stochastic model of the {Cauchy--Robin} problem for systems of nonlinear parabolic equations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {39--71},
     publisher = {mathdoc},
     volume = {515},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2022_515_a3/}
}
TY  - JOUR
AU  - Ya. I. Belopolskaya
TI  - Stochastic model of the Cauchy--Robin problem for systems of nonlinear parabolic equations
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2022
SP  - 39
EP  - 71
VL  - 515
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2022_515_a3/
LA  - ru
ID  - ZNSL_2022_515_a3
ER  - 
%0 Journal Article
%A Ya. I. Belopolskaya
%T Stochastic model of the Cauchy--Robin problem for systems of nonlinear parabolic equations
%J Zapiski Nauchnykh Seminarov POMI
%D 2022
%P 39-71
%V 515
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2022_515_a3/
%G ru
%F ZNSL_2022_515_a3
Ya. I. Belopolskaya. Stochastic model of the Cauchy--Robin problem for systems of nonlinear parabolic equations. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 33, Tome 515 (2022), pp. 39-71. http://geodesic.mathdoc.fr/item/ZNSL_2022_515_a3/