# A pathwise solution for nonlinear parabolic equations with stochastic perturbations

Bogdan Iftimie; Constantin Varsan

Open Mathematics (2003)

- Volume: 1, Issue: 3, page 367-381
- ISSN: 2391-5455

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topBogdan Iftimie, and Constantin Varsan. "A pathwise solution for nonlinear parabolic equations with stochastic perturbations." Open Mathematics 1.3 (2003): 367-381. <http://eudml.org/doc/268809>.

@article{BogdanIftimie2003,

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.},

author = {Bogdan Iftimie, Constantin Varsan},

journal = {Open Mathematics},

keywords = {60H15},

language = {eng},

number = {3},

pages = {367-381},

title = {A pathwise solution for nonlinear parabolic equations with stochastic perturbations},

url = {http://eudml.org/doc/268809},

volume = {1},

year = {2003},

}

TY - JOUR

AU - Bogdan Iftimie

AU - Constantin Varsan

TI - A pathwise solution for nonlinear parabolic equations with stochastic perturbations

JO - Open Mathematics

PY - 2003

VL - 1

IS - 3

SP - 367

EP - 381

AB - 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.

LA - eng

KW - 60H15

UR - http://eudml.org/doc/268809

ER -

## References

top- [1] Pierre Lions and Panagiotis E. Souganidis: Uniqueness of weak solutions of fully nonlinear stochastic partial differential equations, C.R. Acad. Sci., Paris, t.331, Série I, 2000, pp. 783–790. Zbl0970.60072
- [2] Bogdan Iftimie: Qualitative Theory for Diffusion Equations with Applications in Physics, Economy and Techniques, Doctoral Thesis, Institute of Mathematics, Romanian Academy of Sciences, 2001.
- [3] R. Racke: Lectures on Nonlinear Evolution Equations, Aspects of Mathematics, Vieweg, Berlin, 1992.
- [4] Constantin Varsan: On Evolution Systems of Differential Equations with Stochastic Perturbations, Preprint No. 4/2001, IMAR, ISSN-02503638.
- [5] Constantin Varsan: Applications of Lie Algebras to Hyperbolic and Stochastic Differential Equations, Kluwer Academic Publishers, Holland, 1999.
- [6] Constantin Varsan and Cristina Sburlan: Basics of Equations of Mathematical Physics and Differential Equations, Ex Ponto, Constantza, 2000.

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