scholarly journals Cauchy problem of hyperbolic conservation laws in multidimensional space with intersecting jump initial data

1988 ◽  
Vol 307 (2) ◽  
pp. 799-799 ◽  
Author(s):  
De Ning Li
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Multidimensional Space ◽  
Hyperbolic Conservation

Cauchy problem for hyperbolic conservation laws with a relaxation term

1996 ◽  
Vol 126 (4) ◽  
pp. 821-828 ◽  
Author(s):  
Christian Klingenberg ◽  
Yun-guang Lu
Keyword(s):  
Cauchy Problem ◽  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Original System ◽  
Young Measures ◽  
Weak Continuity ◽  
Hyperbolic Conservation ◽  
Relaxation Term ◽  
The Cauchy Problem ◽  
Image Position

This paper considers the Cauchy problem for hyperbolic conservation laws arising in chromatography:with bounded measurable initial data, where the relaxation term g(δ, u, v) converges to zero as the parameter δ > 0 tends to zero. We show that a solution of the equilibrium equationis given by the limit of the solutions of the viscous approximationof the original system as the dissipation ε and the relaxation δ go to zero related by δ = O(ε). The proof of convergence is obtained by a simplified method of compensated compactness [2], avoiding Young measures by using the weak continuity theorem (3.3) of two by two determinants.

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