Wyniki wyszukiwania - BazTech

Ograniczanie wyników

2 2006

Znaleziono wyników: 2

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: równania Burgersa

Sortuj według:

Ogranicz wyniki do:

On support and invariance theorems for a stochastic system of Burgers equtions

Nowak A., Twardowska K.

Demonstratio Mathematica

2006

Vol. 39, nr 3

691-710

We prove a support theorem for a stochastic version of the Burgers system formulated for the deterministic case by Burgers in [Bu 39]. The existence and uniqueness theorem for such a stochastic system was given by Zabczyk and Twardowska in [TZ 06]. In the proof of our support theorem we use a Wong-Zakai type theorem for such a system proved by Nowak in [No 05]. We generalize the method of Mackevicius ([Ma 85]}, [Ma 86]) and Gyongy ([Gy 89]) to prove the support theorem for our stochastic system of Burgers equations. We also use some considerations from Twardowska [Tw 97a]. In our proof of the invariance theorem we use some result of Jachimiak from [Ja 98].

On the extension of Lie group analysis to functional differential equations

Oberlack M., Wacławczyk M.

Archives of Mechanics

2006

Vol. 58, nr 6

597-618

In the present paper the classical point symmetry analysis is extended from partial differential to functional differential equations. In order to perform the group analysis and deal with the functional derivatives, we extend the quantities such as infinitesimal transformations, prolongations and invariant solutions. For the sake of example, the procedure is applied to the functional formulation of the Burgers equation. The method can further lead to important applications in continuum mechanics.