Nonlinear stability of the initial-boundary value problem for the broadwell model around a Maxwellian

Huey Er Lin

doi:10.1142/S0219891611002354

Nonlinear stability of the initial-boundary value problem for the broadwell model around a Maxwellian

Huey Er Lin^*

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We study the nonlinear stability of the equilibrium state associated with the initial boundary value problem for the Broadwell model with transonic boundary. Based on the Green's function of this linearized initial boundary value problem and on the understanding of its action on microscopic data, we establish the pointwise convergence of the solution toward the equilibrium state under small perturbation, via a solution representation and Picard-like iterations.

Original language	English
Pages (from-to)	131-157
Number of pages	27
Journal	Journal of Hyperbolic Differential Equations
Volume	8
Issue number	1
DOIs	https://doi.org/10.1142/S0219891611002354
Publication status	Published - 2011 Mar

Keywords

Green's function
Initial boundary value problem
nonlinear stability

ASJC Scopus subject areas

Analysis
General Mathematics

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10.1142/S0219891611002354

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abstract = "We study the nonlinear stability of the equilibrium state associated with the initial boundary value problem for the Broadwell model with transonic boundary. Based on the Green's function of this linearized initial boundary value problem and on the understanding of its action on microscopic data, we establish the pointwise convergence of the solution toward the equilibrium state under small perturbation, via a solution representation and Picard-like iterations.",

keywords = "Green's function, Initial boundary value problem, nonlinear stability",

author = "Lin, {Huey Er}",

note = "Funding Information: The author would like to thank Professor Tai-Ping Liu and Professor Shih-Hsien Yu for the valuable discussions and suggestions and the referees for the constructive suggestions. The research of the author is supported by NSC 99-2115-M-003-002.",

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doi = "10.1142/S0219891611002354",

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AU - Lin, Huey Er

N1 - Funding Information: The author would like to thank Professor Tai-Ping Liu and Professor Shih-Hsien Yu for the valuable discussions and suggestions and the referees for the constructive suggestions. The research of the author is supported by NSC 99-2115-M-003-002.

PY - 2011/3

Y1 - 2011/3

N2 - We study the nonlinear stability of the equilibrium state associated with the initial boundary value problem for the Broadwell model with transonic boundary. Based on the Green's function of this linearized initial boundary value problem and on the understanding of its action on microscopic data, we establish the pointwise convergence of the solution toward the equilibrium state under small perturbation, via a solution representation and Picard-like iterations.

AB - We study the nonlinear stability of the equilibrium state associated with the initial boundary value problem for the Broadwell model with transonic boundary. Based on the Green's function of this linearized initial boundary value problem and on the understanding of its action on microscopic data, we establish the pointwise convergence of the solution toward the equilibrium state under small perturbation, via a solution representation and Picard-like iterations.

KW - Green's function

KW - Initial boundary value problem

KW - nonlinear stability

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Nonlinear stability of the initial-boundary value problem for the broadwell model around a Maxwellian

Abstract

Keywords

ASJC Scopus subject areas

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