ASYMPTOTIC STABILITY OF RAREFACTION WAVE FOR THE INFLOW PROBLEM GOVERNED BY THE ONE-DIMENSIONAL RADIATIVE EULER EQUATIONS

Lili FAN; LIzhi RUAN; Wei XIANG

doi:10.1137/18M1203043

ASYMPTOTIC STABILITY OF RAREFACTION WAVE FOR THE INFLOW PROBLEM GOVERNED BY THE ONE-DIMENSIONAL RADIATIVE EULER EQUATIONS

Lili FAN
, LIzhi RUAN^*
, Wei XIANG

^*Corresponding author for this work

Department of Mathematics

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

22 Citations (Scopus)

42 Downloads (CityUHK Scholars)

Abstract

This paper is devoted to the study of the initial-boundary value problem on the half line for a one-dimensional radiative Euler equations, which is a system coupled by the classic compressible nonisentropic Euler equations with an elliptic equation. In particular, we focus our attention on the inflow problem when the velocity of the inward flow on the boundary is given as a positive constant. We give a rigorous proof of the asymptotic stability of the rarefaction wave without restrictions on the smallness of the wave strength, provided that the data on the boundary is supersonic. It is the first rigorous result on the initial-boundary value problem for the radiative Euler equations. New and subtle analysis is developed to overcome difficulties due to the boundary effect to derive energy estimates.

Original language	English
Pages (from-to)	595-625
Journal	SIAM Journal on Mathematical Analysis
Volume	51
Issue number	1
Online published	28 Feb 2019
DOIs	https://doi.org/10.1137/18M1203043
Publication status	Published - 2019

Funding

The research of Lili Fan was supported in part by the Natural Science Foundation of China, 11871388, 11701439, and by the Fundamental Research Grants from the Science Foundation of Hubei Province under contract 2018CFB693. The research of Lizhi Ruan was supported in part by the Natural Science Foundation of China, 11771169, 11331005, 11871236, 11301205; the Program for Changjiang Schol- ars and Innovative Research Team in University, IRT17R46; and the Special Fund for Basic Scientific Research of Central Colleges, CCNU18CXTD04. The research of Wei Xiang was supported in part by the Research Grants Council of the HKSAR, China (Project CityU 21305215, Project CityU 11332916, Project CityU 11304817, and Project CityU 11303518).

Research Keywords

radiative Euler equations
inflow problem
rarefaction wave

Publisher's Copyright Statement

COPYRIGHT TERMS OF DEPOSITED FINAL PUBLISHED VERSION FILE: © 2019 Society for Industrial and Applied Mathematics.

RGC Funding Information

RGC-funded

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title = "ASYMPTOTIC STABILITY OF RAREFACTION WAVE FOR THE INFLOW PROBLEM GOVERNED BY THE ONE-DIMENSIONAL RADIATIVE EULER EQUATIONS",

abstract = "This paper is devoted to the study of the initial-boundary value problem on the half line for a one-dimensional radiative Euler equations, which is a system coupled by the classic compressible nonisentropic Euler equations with an elliptic equation. In particular, we focus our attention on the inflow problem when the velocity of the inward flow on the boundary is given as a positive constant. We give a rigorous proof of the asymptotic stability of the rarefaction wave without restrictions on the smallness of the wave strength, provided that the data on the boundary is supersonic. It is the first rigorous result on the initial-boundary value problem for the radiative Euler equations. New and subtle analysis is developed to overcome difficulties due to the boundary effect to derive energy estimates.",

keywords = "radiative Euler equations, inflow problem, rarefaction wave",

author = "Lili FAN and LIzhi RUAN and Wei XIANG",

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T1 - ASYMPTOTIC STABILITY OF RAREFACTION WAVE FOR THE INFLOW PROBLEM GOVERNED BY THE ONE-DIMENSIONAL RADIATIVE EULER EQUATIONS

AU - FAN, Lili

AU - RUAN, LIzhi

AU - XIANG, Wei

PY - 2019

Y1 - 2019

N2 - This paper is devoted to the study of the initial-boundary value problem on the half line for a one-dimensional radiative Euler equations, which is a system coupled by the classic compressible nonisentropic Euler equations with an elliptic equation. In particular, we focus our attention on the inflow problem when the velocity of the inward flow on the boundary is given as a positive constant. We give a rigorous proof of the asymptotic stability of the rarefaction wave without restrictions on the smallness of the wave strength, provided that the data on the boundary is supersonic. It is the first rigorous result on the initial-boundary value problem for the radiative Euler equations. New and subtle analysis is developed to overcome difficulties due to the boundary effect to derive energy estimates.

AB - This paper is devoted to the study of the initial-boundary value problem on the half line for a one-dimensional radiative Euler equations, which is a system coupled by the classic compressible nonisentropic Euler equations with an elliptic equation. In particular, we focus our attention on the inflow problem when the velocity of the inward flow on the boundary is given as a positive constant. We give a rigorous proof of the asymptotic stability of the rarefaction wave without restrictions on the smallness of the wave strength, provided that the data on the boundary is supersonic. It is the first rigorous result on the initial-boundary value problem for the radiative Euler equations. New and subtle analysis is developed to overcome difficulties due to the boundary effect to derive energy estimates.

KW - radiative Euler equations

KW - inflow problem

KW - rarefaction wave

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U2 - 10.1137/18M1203043

DO - 10.1137/18M1203043

M3 - RGC 21 - Publication in refereed journal

SN - 0036-1410

VL - 51

SP - 595

EP - 625

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 1

ER -

ASYMPTOTIC STABILITY OF RAREFACTION WAVE FOR THE INFLOW PROBLEM GOVERNED BY THE ONE-DIMENSIONAL RADIATIVE EULER EQUATIONS

Abstract

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GRF: Discontinuous Compressible Flows Onto Solid Objects

ECS: Shock Diffraction/Reflection and Related Problems in Multi-Dimensional Conservation Laws

Cite this

ASYMPTOTIC STABILITY OF RAREFACTION WAVE FOR THE INFLOW PROBLEM GOVERNED BY THE ONE-DIMENSIONAL RADIATIVE EULER EQUATIONS

Abstract

Funding

Research Keywords

Publisher's Copyright Statement

RGC Funding Information

Access Output

Other Access Options

Permanent Link

Other Files and Links

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Projects

GRF: Discontinuous Compressible Flows Onto Solid Objects

ECS: Shock Diffraction/Reflection and Related Problems in Multi-Dimensional Conservation Laws

Cite this