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A pathwise solution for nonlinear parabolic equations with stochastic perturbations

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Iftimie B., Varsan C.

Open Mathematics

2003

tom 1

nr 3

367-381

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.

Ograniczanie wyników

1 Open Mathematics

1 Iftimie B.

1 Varsan C.

1 2003

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A pathwise solution for nonlinear parabolic equations with stochastic perturbations