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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Vespri, Vincenzo / Marano, Salvatore Angelo

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Volume 1, Issue 3


Volume 13 (2015)

A pathwise solution for nonlinear parabolic equations with stochastic perturbations

Bogdan Iftimie / Constantin Varsan
Published Online: 2003-09-01 | DOI: https://doi.org/10.2478/BF02475216


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: stochastic partial differential equations (SPDE); finite dimensional Lie algebras

Keywords: 60H15

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  • [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. Google Scholar

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  • [5] Constantin Varsan: Applications of Lie Algebras to Hyperbolic and Stochastic Differential Equations, Kluwer Academic Publishers, Holland, 1999. Google Scholar

  • [6] Constantin Varsan and Cristina Sburlan: Basics of Equations of Mathematical Physics and Differential Equations, Ex Ponto, Constantza, 2000. Google Scholar

About the article

Published Online: 2003-09-01

Published in Print: 2003-09-01

Citation Information: Open Mathematics, Volume 1, Issue 3, Pages 367–381, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/BF02475216.

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© 2003 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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