A pathwise solution for nonlinear parabolic equations with stochastic perturbations

• Autorzy: Bogdan Iftimie , Constantin Varsan
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

stochastic partial differential equations (SPDE); finite dimensional Lie algebras; 60H15

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2003
• Tom: 1
• Numer: 3
• Strony: 367-381

Daty

wydano

2003-09-01

online

2003-09-01

Twórcy

autor

Bogdan Iftimie

• Academy of Economic Sciences

autor

Constantin Varsan

• Institute of Mathematics “Simion Stoilow” of the Romanian Academy

Bibliografia

• [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.
• [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.

Identyfikatory

DOI

10.2478/BF02475216