GLOBAL SOLUTIONS FOR THE 1-D COMPRESSIBLE EULER EQUATIONS WITH TIME-DEPENDENT DAMPING

被引：0

作者：

Chen, Shaohua ^{[1
]}

机构：

[1] Cape Breton Univ, Sch Sci & Technol, Sydney, NS B1P 6L2, Canada

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2024年 / 23卷 / 01期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Compressible Euler equations; hyperbolic p-system; Time-gradually-degenerate damping; Global existence; NONLINEAR DIFFUSION WAVES; HYPERBOLIC CONSERVATION-LAWS; CONVERGENCE-RATES; P-SYSTEM; SINGULARITY FORMATION; ASYMPTOTIC-BEHAVIOR; POISSON EQUATIONS; EXISTENCE;

D O I：

10.3934/cpaa.2023125

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we investigate the Cauchy problem for the 1-D compressible Euler equations with time-dependent damping. We prove the existence of global solutions under the assumptions that the derivatives of initial data are suitable small and the initial specific volume is large without the condition of small perturbations to the constant initial data. Our approach is based on estimates of the derivatives of Riemann invariants along two characteristic curves.

引用

页码：1 / 20

页数：20

共 33 条

[1] SINGULARITY FORMATION FOR THE COMPRESSIBLE EULER EQUATIONS [J].

Chen, Geng ;

Pan, Ronghua ;

Zhu, Shengguo .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2017, 49 (04) :2591-2614

[2] Global and blow-up solutions for compressible Euler equations with time-dependent damping [J].

Chen, Shaohua ;

Li, Haitong ;

Li, Jingyu ;

Mei, Ming ;

Zhang, Kaijun .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2020, 268 (09) :5035-5077

[3] Convergence to nonlinear diffusion waves for solutions of Euler equations with time-depending damping [J].

Cui, Haibo ;

Yin, Haiyan ;

Zhang, Jinshun ;

Zhu, Changjiang .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2018, 264 (07) :4564-4602

[4] Initial-boundary value problem for p-system with damping in half space [J].

Deng, Shijin .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2016, 143 :193-210

[5] Blow-up for compressible Euler system with space-dependent damping in 1-D [J].

Geng, Jinbo ;

Lai, Ning-An ;

Yuen, Manwai ;

Zhou, Jiang .

ADVANCES IN NONLINEAR ANALYSIS, 2023, 12 (01)

[6] ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO EULER EQUATIONS WITH TIME-DEPENDENT DAMPING IN CRITICAL CASE [J].

Geng, Shifeng ;

Lin, Yanping ;

Mei, Ming .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2020, 52 (02) :1463-1488

[7] Convergence Rates to Nonlinear Diffusion Waves for Solutions to the System of Compressible Adiabatic Flow through Porous Media [J].

Geng, Shifeng ;

Wang, Zhen .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2011, 36 (05) :850-872

[8] CONVERGENCE TO NONLINEAR DIFFUSION WAVES FOR SOLUTIONS OF A SYSTEM OF HYPERBOLIC CONSERVATION-LAWS WITH DAMPING [J].

HSIAO, L ;

LIU, TP .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1992, 143 (03) :599-605

[9] OPTIMAL DECAY RATES OF THE COMPRESSIBLE EULER EQUATIONS WITH TIME-DEPENDENT DAMPING IN Rn: (II) OVERDAMPING CASE [J].

Ji, Shanming ;

Mei, Ming .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2023, 55 (02) :1048-1099

[10]

Ji SM, 2023, J NONLINEAR SCI, V33, DOI 10.1007/s00332-022-09865-y

← 1 2 3 4 →