scholarly journals Asymptotic stability of relaxation shock profiles for hyperbolic conservation laws

2003 ◽  
Vol 192 (2) ◽  
pp. 285-307 ◽  
Author(s):  
Hailiang Liu
Keyword(s):  
Asymptotic Stability ◽  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Hyperbolic Conservation ◽  
Shock Profiles

Linear stability of shock profiles for a quasilinear Benney system in ℝ2 × ℝ+

2020 ◽  
Vol 17 (04) ◽  
pp. 797-807
Author(s):  
João-Paulo Dias
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Short Wave ◽  
Wave Interactions ◽  
Hyperbolic Conservation ◽  
Linearized Stability ◽  
Shock Profiles ◽  
Scalar Conservation ◽  
Semilinear Schrödinger Equation ◽  
Shock Profile

Following Dias et al. [Vanishing viscosity with short wave-long wave interactions for multi-D scalar conservation laws, J. Differential Equations 251 (2007) 555–563], we study the linearized stability of a pair [Formula: see text], where [Formula: see text] is a shock profile for a family of quasilinear hyperbolic conservation laws in [Formula: see text] coupled with a semilinear Schrödinger equation.

VISCOUS SHOCK PROFILES FOR 2 × 2 SYSTEMS OF HYPERBOLIC CONSERVATION LAWS WITH AN UMBILIC POINT

2009 ◽  
Vol 06 (03) ◽  
pp. 483-524
Author(s):  
FUMIOKI ASAKURA ◽  
MITSURU YAMAZAKI
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Propagation Speed ◽  
Umbilic Point ◽  
Hyperbolic Conservation ◽  
Reservoir Flow ◽  
Viscous Profile ◽  
Systems Of Conservation Laws ◽  
Shock Profiles ◽  
Shock Profile

This article analyzes the existence of viscous shock profiles joining two states satisfying the Rankine–Hugoniot condition that comes from hyperbolic 2 × 2 systems of conservation laws having quadratic flux functions with an isolated umbilic point: the point where the characteristic speeds coincide and the Jacobian matrix of the flux functions is diagonalizable. The systems studied in this note are particularly in Schaeffer and Shearer's cases I and II which are relevant to the three-phase Buckley–Leverett model for oil reservoir flow. It is shown that any compressive and overcompressive shocks have a viscous shock profile provided that there are no undercompressive shock with viscous profile having the same propagation speed. The idea of the proof is a generalization of the first theorem of Morse to noncompact level sets. It is also shown that there exists a shock satisfying the Liu–Oleĭnik condition but having no viscous shock profile. In this case, there is an undercompressive shock with viscous shock profile.

scholarly journals High order explicit local time stepping methods for hyperbolic conservation laws

2020 ◽  
Vol 89 (324) ◽  
pp. 1807-1842
Author(s):  
Thi-Thao-Phuong Hoang ◽  
Lili Ju ◽  
Wei Leng ◽  
Zhu Wang
Keyword(s):  
Conservation Laws ◽  
Local Time ◽  
Hyperbolic Conservation Laws ◽  
High Order ◽  
Hyperbolic Conservation ◽  
Time Stepping ◽  
Local Time Stepping
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