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

Abstract

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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.

How to cite

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Bogdan 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

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  1. [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. [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. [3] R. Racke: Lectures on Nonlinear Evolution Equations, Aspects of Mathematics, Vieweg, Berlin, 1992. 
  4. [4] Constantin Varsan: On Evolution Systems of Differential Equations with Stochastic Perturbations, Preprint No. 4/2001, IMAR, ISSN-02503638. 
  5. [5] Constantin Varsan: Applications of Lie Algebras to Hyperbolic and Stochastic Differential Equations, Kluwer Academic Publishers, Holland, 1999. 
  6. [6] Constantin Varsan and Cristina Sburlan: Basics of Equations of Mathematical Physics and Differential Equations, Ex Ponto, Constantza, 2000. 

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