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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access September 1, 2003

A pathwise solution for nonlinear parabolic equations with stochastic perturbations

Bogdan Iftimie and Constantin Varsan
From the journal Open Mathematics

Abstract

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.

Keywords: 60H15

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Published Online: 2003-9-1
Published in Print: 2003-9-1

© 2003 Versita Warsaw

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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