We consider conditional propagation of chaos and use it to solve a class of quasilinear equations of parabolic type. In addition, we construct a class of continuous stochastic processes associated with the above nonlinear equations. Our method imposes fewer smoothness conditions on the coefficients and allows a degenerate nonlinear weight before a divergence form operator. We hope this probabilistic approach will introduce a better microscopic picture for understanding some Stefan type problems.
@article{1176988189,
author = {Zheng, Weian},
title = {Conditional Propagation of Chaos and a Class of Quasilinear PDE'S},
journal = {Ann. Probab.},
volume = {23},
number = {3},
year = {1995},
pages = { 1389-1413},
language = {en},
url = {http://dml.mathdoc.fr/item/1176988189}
}
Zheng, Weian. Conditional Propagation of Chaos and a Class of Quasilinear PDE'S. Ann. Probab., Tome 23 (1995) no. 3, pp. 1389-1413. http://gdmltest.u-ga.fr/item/1176988189/