Displaying similar documents to “Quasi-reductive (bi)parabolic subalgebras in reductive Lie algebras.”

A pathwise solution for nonlinear parabolic equations with stochastic perturbations

Bogdan Iftimie, Constantin Varsan (2003)

Open Mathematics

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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.