Probabilistic Interpretation of the Vanishing Viscosity Method for Systems of Conservation and Balance Laws

2021 ◽  
Vol 109 (3-4) ◽  
pp. 347-357
Author(s):  
Ya. I. Belopol’skaya
Keyword(s):  
Balance Laws ◽  
Probabilistic Interpretation ◽  
Viscosity Method ◽  
Vanishing Viscosity

scholarly journals Vanishing Viscosity Method for Transonic Flow

2008 ◽  
Vol 189 (1) ◽  
pp. 159-188 ◽  
Author(s):  
Gui-Qiang Chen ◽  
Marshall Slemrod ◽  
Dehua Wang
Keyword(s):  
Transonic Flow ◽  
Viscosity Method ◽  
Vanishing Viscosity

COUPLING OF MULTIDIMENSIONAL PARABOLIC AND HYPERBOLIC EQUATIONS

2006 ◽  
Vol 03 (01) ◽  
pp. 53-80 ◽  
Author(s):  
GLORIA AGUILAR ◽  
LAURENT LÉVI ◽  
MONIQUE MADAUNE-TORT
Keyword(s):  
Hyperbolic Equations ◽  
Type Equation ◽  
Entropy Inequality ◽  
Order Operator ◽  
Viscosity Method ◽  
Vanishing Viscosity ◽  
Reaction Type ◽  
First Order ◽  
Definition Of ◽  
Uniqueness Proof

This paper deals with the mathematical analysis of a quasilinear parabolic-hyperbolic problem in a multidimensional bounded domain Ω. In a region Ωp a diffusion-advection-reaction type equation is set, while in the complementary Ωh ≡ Ω\Ωp, only advection-reaction terms are taken into account. To begin we provide a definition of a weak solution through an entropy inequality on the whole domain. Since the interface ∂Ωp ∩ ∂Ωh contains outward characteristics for the first-order operator in Ωh, the uniqueness proof starts by considering first the hyperbolic zone and then the parabolic one. The existence property uses the vanishing viscosity method and to pass to the limit on the hyperbolic zone, we refer to the notion of process solution.

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