Vanishing viscosity limit for Riemann solutions to a 2 x 2 hyperbolic system with linear damping

被引：9
作者：
De la Cruz, Richard [1 ]
Juajibioy, Juan [1 ]
机构：
[1] Univ Pedag & Tecnol Colombia, Sch Math & Stat, Av Cent Norte 39-115 M-101, Tunja 150003, Boyaca, Colombia
来源：
ASYMPTOTIC ANALYSIS | 2022年 / 127卷 / 03期
关键词：
Nonstrictly hyperbolic system; linear damping; Riemann problem; time-dependent viscous system; delta shock wave solution; DELTA-SHOCK-WAVES; MODEL-EQUATIONS; EXISTENCE; BEHAVIOR; DYNAMICS;
D O I：
10.3233/ASY-211690
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we propose a time-dependent viscous system and by using the vanishing viscosity method we show the existence of solutions for the Riemann problem to a particular 2 x 2 system of conservation laws with linear damping.
引用
收藏
页码：275 / 296
页数：22
相关论文
共 29 条
[1]  
Barenblatt G.I., 1996, Scaling, Self-similarity, and Intermediate Asymptotics: Dimensional Analysis and Intermediate Asymptotics, DOI [10.1017/cbo9781107050242, DOI 10.1017/CBO9781107050242, 10.1017/CBO9781107050242]
[2]   ASYMPTOTIC SOLUTIONS OF MODEL EQUATIONS IN NON-LINEAR ACOUSTICS [J].
CRIGHTON, DG ;
SCOTT, JF .
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1979, 292 (1389) :101-134
[3]   MODEL EQUATIONS OF NON-LINEAR ACOUSTICS [J].
CRIGHTON, DG .
ANNUAL REVIEW OF FLUID MECHANICS, 1979, 11 :11-33
[4]  
DAFERMOS CM, 1973, ARCH RATION MECH AN, V52, P1, DOI 10.1007/BF00249087
[5]  
de la Cruz R, 2020, ACTA APPL MATH, V170, P631, DOI 10.1007/s10440-020-00350-w
[6]   Delta shock waves for a system of Keyfitz-Kranzer type [J].
De la cruz, Richard ;
Santos, Marcelo .
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 2019, 99 (03)
[7]   SIMILARITY SOLUTIONS OF A GENERALIZED BURGERS-EQUATION [J].
DOYLE, J ;
ENGLEFIELD, MJ .
IMA JOURNAL OF APPLIED MATHEMATICS, 1990, 44 (02) :145-153
[8]   Delta-shock waves as self-similar viscosity limits [J].
Ercole, G .
QUARTERLY OF APPLIED MATHEMATICS, 2000, 58 (01) :177-199
[9]  
Henriksen RN., 2015, Scale invariance: self-similarity of the physical world, DOI [10.1002/9783527687343, DOI 10.1002/9783527687343]
[10]   ANALYSIS OF A SINGULAR HYPERBOLIC SYSTEM OF CONSERVATION-LAWS [J].
ISAACSON, EL ;
TEMPLE, JB .
JOURNAL OF DIFFERENTIAL EQUATIONS, 1986, 65 (02) :250-268
123