Unique solvability and zero diffusion limits of global large solution for a nonlinear hyperbolic system with damping and diffusion

Andrew YANG; Wenshu ZHOU

doi:10.3934/dcdsb.2023083

Unique solvability and zero diffusion limits of global large solution for a nonlinear hyperbolic system with damping and diffusion

Andrew YANG, Wenshu ZHOU^*

^*Corresponding author for this work

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

Abstract

We consider the Dirichlet-Neumann problem and the spatially periodic Cauchy problem for a nonlinear hyperbolic system with damping and diffusion introduced in [13] for the study of chaos. Firstly, the existence and uniqueness of global solutions with large initial data is established. Then the zero diffusion limits are justified. Moreover, the L² convergence rate in terms of the diffusion coefficient is obtained. Based on a new observation of the structure of the system, two equalities are found to show the existence of global large solutions of the system.

Original language	English
Pages (from-to)	1-21
Number of pages	21
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	29
Issue number	1
Online published	May 2023
DOIs	https://doi.org/10.3934/dcdsb.2023083
Publication status	Published - Jan 2024

Research Keywords

Nonlinear hyperbolic system
global large solution
unique solvability
zero diffusion limit
NAVIER-STOKES EQUATIONS
EVOLUTION-EQUATIONS
BOUNDARY-LAYERS
CAUCHY-PROBLEM
DECAY-RATES
PERTURBATIONS
ASYMPTOTICS
ELLIPTICITY
VISCOSITY
STABILITY

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title = "Unique solvability and zero diffusion limits of global large solution for a nonlinear hyperbolic system with damping and diffusion",

abstract = "We consider the Dirichlet-Neumann problem and the spatially periodic Cauchy problem for a nonlinear hyperbolic system with damping and diffusion introduced in [13] for the study of chaos. Firstly, the existence and uniqueness of global solutions with large initial data is established. Then the zero diffusion limits are justified. Moreover, the L2 convergence rate in terms of the diffusion coefficient is obtained. Based on a new observation of the structure of the system, two equalities are found to show the existence of global large solutions of the system.",

keywords = "Nonlinear hyperbolic system, global large solution, unique solvability, zero diffusion limit, NAVIER-STOKES EQUATIONS, EVOLUTION-EQUATIONS, BOUNDARY-LAYERS, CAUCHY-PROBLEM, DECAY-RATES, PERTURBATIONS, ASYMPTOTICS, ELLIPTICITY, VISCOSITY, STABILITY",

author = "Andrew YANG and Wenshu ZHOU",

year = "2024",

month = jan,

doi = "10.3934/dcdsb.2023083",

language = "English",

volume = "29",

pages = "1--21",

journal = "Discrete and Continuous Dynamical Systems - Series B",

issn = "1531-3492",

publisher = "AIMS Press",

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TY - JOUR

T1 - Unique solvability and zero diffusion limits of global large solution for a nonlinear hyperbolic system with damping and diffusion

AU - YANG, Andrew

AU - ZHOU, Wenshu

PY - 2024/1

Y1 - 2024/1

N2 - We consider the Dirichlet-Neumann problem and the spatially periodic Cauchy problem for a nonlinear hyperbolic system with damping and diffusion introduced in [13] for the study of chaos. Firstly, the existence and uniqueness of global solutions with large initial data is established. Then the zero diffusion limits are justified. Moreover, the L2 convergence rate in terms of the diffusion coefficient is obtained. Based on a new observation of the structure of the system, two equalities are found to show the existence of global large solutions of the system.

AB - We consider the Dirichlet-Neumann problem and the spatially periodic Cauchy problem for a nonlinear hyperbolic system with damping and diffusion introduced in [13] for the study of chaos. Firstly, the existence and uniqueness of global solutions with large initial data is established. Then the zero diffusion limits are justified. Moreover, the L2 convergence rate in terms of the diffusion coefficient is obtained. Based on a new observation of the structure of the system, two equalities are found to show the existence of global large solutions of the system.

KW - Nonlinear hyperbolic system

KW - global large solution

KW - unique solvability

KW - zero diffusion limit

KW - NAVIER-STOKES EQUATIONS

KW - EVOLUTION-EQUATIONS

KW - BOUNDARY-LAYERS

KW - CAUCHY-PROBLEM

KW - DECAY-RATES

KW - PERTURBATIONS

KW - ASYMPTOTICS

KW - ELLIPTICITY

KW - VISCOSITY

KW - STABILITY

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DO - 10.3934/dcdsb.2023083

M3 - RGC 21 - Publication in refereed journal

SN - 1531-3492

VL - 29

SP - 1

EP - 21

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

IS - 1

ER -

Unique solvability and zero diffusion limits of global large solution for a nonlinear hyperbolic system with damping and diffusion

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