2. The Vanishing Viscosity Method of Some Nonlinear Evolution System

2016 ◽  
pp. 39-232
Keyword(s):  
Nonlinear Evolution ◽  
Evolution System ◽  
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

On coupled nonlinear evolution system of fractional order with a proportional delay

2021 ◽  
Author(s):  
Israr Ahmad ◽  
Hussam Alrabaiah ◽  
Kamal Shah ◽  
Juan J. Nieto ◽  
Ibrahim Mahariq ◽  
...  
Keyword(s):  
Fractional Order ◽  
Nonlinear Evolution ◽  
Proportional Delay ◽  
Evolution System

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.

Spectral broadening and flow randomization in free shear layers

2012 ◽  
Vol 706 ◽  
pp. 431-469 ◽  
Author(s):  
Xuesong Wu ◽  
Feng Tian
Keyword(s):  
Phase Modulation ◽  
Numerical Solutions ◽  
Nonlinear Evolution ◽  
Present Theory ◽  
Shear Layers ◽  
Evolution System ◽  
Free Shear Layer ◽  
Spectral Broadening ◽  
Free Shear Layers ◽  
Combination Frequencies

AbstractIt has been observed experimentally that when a free shear layer is perturbed by a disturbance consisting of two waves with frequencies ${\omega }_{0} $ and ${\omega }_{1} $, components with the combination frequencies $(m{\omega }_{0} \pm n{\omega }_{1} )$ ($m$ and $n$ being integers) develop to a significant level thereby causing flow randomization. This spectral broadening process is investigated theoretically for the case where the frequency difference $({\omega }_{0} \ensuremath{-} {\omega }_{1} )$ is small, so that the perturbation can be treated as a modulated wavetrain. A nonlinear evolution system governing the spectral dynamics is derived by using the non-equilibrium nonlinear critical layer approach. The formulation provides an appropriate mathematical description of the physical concepts of sideband instability and amplitude–phase modulation, which were suggested by experimentalists. Numerical solutions of the nonlinear evolution system indicate that the present theory captures measurements and observations rather well.

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