Convergence rates of vanishing diffusion limit on nonlinear hyperbolic system with damping and diffusion

2012 ◽  
Vol 53 (10) ◽  
pp. 103703
Author(s):  
Lizhi Ruan ◽  
Haiyan Yin
Keyword(s):  
Hyperbolic System ◽  
Convergence Rates ◽  
Diffusion Limit ◽  
Nonlinear Hyperbolic System ◽  
And Diffusion

THE ZERO DIFFUSION LIMIT FOR NONLINEAR HYPERBOLIC SYSTEM WITH DAMPING AND DIFFUSION

2008 ◽  
Vol 05 (04) ◽  
pp. 767-783 ◽  
Author(s):  
KAIMAO CHEN ◽  
CHANGJIANG ZHU
Keyword(s):  
Hyperbolic System ◽  
Existence Of Solutions ◽  
Diffusion Limit ◽  
Linear Diffusion ◽  
Diffusion Waves ◽  
Global Existence Of Solutions ◽  
Nonlinear Hyperbolic System ◽  
The Cauchy Problem ◽  
Zero Diffusion Limit ◽  
And Diffusion

We consider the Cauchy problem for a nonlinear hyperbolic system with damping and diffusion. Thanks to a suitably constructed corrector function, we can eliminate the layer at infinity and by using the energy method we establish the global existence of solutions if the initial data is a small perturbation around the corresponding linear diffusion waves. Furthermore, we study the zero diffusion limit and, precisely, we show that the sequence of solutions converges to the corresponding hyperbolic system as the diffusion parameter tends to zero.

Computational Models on Graphs for the Nonlinear Hyperbolic System of Equations

2004 ◽  
Author(s):  
Alexander S. Kholodov ◽  
Yaroslav A. Kholodov
Keyword(s):  
Hyperbolic System ◽  
Human Body ◽  
Partial Derivative ◽  
Computational Models ◽  
Heavy Traffic ◽  
Large River ◽  
System Of Equations ◽  
Information Flows ◽  
Flood Water ◽  
Nonlinear Hyperbolic System

The problems in the form of nonlinear partial derivative equations on graphs (nets, trees) arise in different applications. As the examples of such models we can name the circulatory and respiratory systems of the human body, the model of heavy traffic in the big cities, the model of flood water and pollution propagation in the large river systems, the model of bar structures and frames behavior under the different impacts, the model of the intensive information flows in the computer networks and others.

REFRACTION AND DIFFUSION OF ACOUSTIC WAVES IN A RANDOM FLUID MEDIUM

2002 ◽  
Vol 10 (02) ◽  
pp. 265-274
Author(s):  
JEONG-HOON KIM
Keyword(s):  
Acoustic Waves ◽  
Wave Equations ◽  
Planck Equation ◽  
Diffusion Limit ◽  
Fluid Medium ◽  
Limit Theory ◽  
Probabilistic Distribution ◽  
Wave Propagation Problem ◽  
Propagating Waves ◽  
And Diffusion

Based upon the asymptotic and stochastic formulation of the acoustic wave equations, this article considers a stochastic wave propagation problem in a random multilayer which is totally refracting. Both the WKB analysis and the diffusion limit theory of stochastic differential equations are used to analyze the interplay of refraction (macrostructure) and diffusion (microstructure) of the propagating waves. The probabilistic distribution of solutions to the resultant Kolmogorov–Fokker–Planck equation is given as a computable form from the pseudodifferential operator theory and Wiener's path integral theory.

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