We analyse here a semilinear stochastic partial differential equation of parabolic type where the diffusion vector fields are depending on both the unknown function and its gradient ∂ xu with respect to the state variable, ∈ ℝn. A local solution is constructed by reducing the original equation to a nonlinear parabolic one without stochastic perturbations and it is based on a finite dimensional Lie algebra generated by the given diffusion vector fields.
@article{bwmeta1.element.doi-10_2478_BF02475216,
author = {Bogdan Iftimie and Constantin Varsan},
title = {A pathwise solution for nonlinear parabolic equations with stochastic perturbations},
journal = {Open Mathematics},
volume = {1},
year = {2003},
pages = {367-381},
zbl = {1031.35156},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475216}
}
Bogdan Iftimie; Constantin Varsan. A pathwise solution for nonlinear parabolic equations with stochastic perturbations. Open Mathematics, Tome 1 (2003) pp. 367-381. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475216/
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