The Korteweg–de Vries–Burgers hierarchy in fluid-filled elastic tubes

In this work we study wave propagation in dissipative relativistic fluids described by a simplified set of the 2nd order viscous conformal hydrodynamic equations corresponding to Israel-Stewart theory. Small amplitude waves are studied within the linearization approximation while waves with large amplitude are investigated using the reductive perturbation method, which is generalized to the case of 2nd order relativistic hydrodynamics. Our results indicate the presence of a "soliton-like" wave solution in Israel-Stewart hydrodynamics despite the presence of dissipation and relaxation effects.

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“…We also change the shear viscosity coefficient and the relaxation time to the (X, Y ) space in the following way [38,39] η = σ 1/2η and…”

Section: A Reductive Perturbation Methodsmentioning

confidence: 99%

Nonlinear waves in second order conformal hydrodynamics

et al. 2015

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“…where L is a characteristic length scale of the problem (typically the radius of a heavy ion) and σ is a small (0 < σ < 1) expansion parameter. We also perform the following transformation of the viscosity coefficients [45,46]:…”

Section: B Nonlinear Waves In a Hadron Gasmentioning

confidence: 99%

Viscosity, wave damping, and shock-wave formation in cold hadronic matter

2013

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We study linear and nonlinear wave propagation in a dense and cold hadron gas and also in a cold quark-gluon plasma, taking viscosity into account and using the Navier-Stokes equation. The equation of state of the hadronic phase is derived from the nonlinear Walecka model in the mean-field approximation. The quark-gluon plasma phase is described by the MIT equation of state. We show that in a hadron gas viscosity strongly damps wave propagation and also hinders shock-wave formation. This marked difference between the two phases may have phenomenological consequences and lead to new quark-gluon plasma signatures.

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“…is equation is useful in modeling many physical phenomena such as the unidirectional propagation of planar waves [33], strain waves and longitudinal deformation in a nonlinear elastic rod [34], and pressure waves in a liquid-gas bubble mixture [5]. Note that there has been a growing interest in the analysis and control of the GKdVB equation [2,33,[35][36][37][38][39][40][41]. Specifically, long-time behavior of periodic solutions of the GKdVB equation has been investigated [2].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Adaptive Boundary Control of the Modified Generalized Korteweg–de Vries–Burgers Equation

2020

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In this paper, we study the nonlinear adaptive boundary control problem of the modified generalized Korteweg–de Vries–Burgers equation (MGKdVB) when the spatial domain is 0,1. Four different nonlinear adaptive control laws are designed for the MGKdVB equation without assuming the nullity of the physical parameters ν, μ, γ1, and γ2 and depending whether these parameters are known or unknown. Then, using Lyapunov theory, the L2-global exponential stability of the solution is proven in each case. Finally, numerical simulations are presented to illustrate the developed control schemes.

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The Korteweg–de Vries–Burgers hierarchy in fluid-filled elastic tubes

Cited by 16 publications

References 21 publications

Nonlinear waves in second order conformal hydrodynamics

Nonlinear waves in second order conformal hydrodynamics

Viscosity, wave damping, and shock-wave formation in cold hadronic matter

Nonlinear Adaptive Boundary Control of the Modified Generalized Korteweg–de Vries–Burgers Equation

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