A viscosity approximation to a system of conservation laws with no classical Riemann solution

1989 ◽  
pp. 185-197 ◽  
Author(s):  
Barbara Lee Keyfitz ◽  
Herbert C. Kranzer
Keyword(s):  
Conservation Laws ◽  
Viscosity Approximation ◽  
Riemann Solution ◽  
System Of Conservation Laws

The Riemann problem for a resonant nonlinear system of conservation laws with Dirac-measure solutions

1998 ◽  
Vol 128 (1) ◽  
pp. 81-94 ◽  
Author(s):  
Jiaxin Hu
Keyword(s):  
Nonlinear System ◽  
Conservation Laws ◽  
Riemann Problem ◽  
Additional Condition ◽  
Dirac Measure ◽  
Viscosity Approximation ◽  
Riemann Solution ◽  
System Of Conservation Laws ◽  
Genuine Nonlinearity ◽  
Contact Wave

The Riemann problem for a resonant nonlinear system of conservation laws is considered here. The Riemann solution was constructed by employing the viscosity approximation approach. One kind of new discontinuity, which is called the Dirac-contact wave, appeared in the Riemann solution. Because the strict hyperbolicity as well as the genuine nonlinearity of the system considered failed, the solution we obtained in this paper is not unique for some initial data. An additional condition was explored to guarantee the uniqueness of the Riemann problem.

A difference scheme for a stiff system of conservation laws

1998 ◽  
Vol 128 (6) ◽  
pp. 1403-1414 ◽  
Author(s):  
Wen-An Yong
Keyword(s):  
Relaxation Time ◽  
Difference Scheme ◽  
Conservation Laws ◽  
Difference Method ◽  
Initial Value Problems ◽  
Equilibrium System ◽  
Initial Value ◽  
Stiff System ◽  
System Of Conservation Laws ◽  
Entropy Satisfying

A stiff system of conservation laws is analysed using a difference method. The existence of entropy-satisfying BV-solutions to the initial value problems is established. Furthermore, we show that the solutions converge to the solutions of the corresponding equilibrium system as the relaxation time tends to zero.

Sign in / Sign up

Export Citation Format

Share Document