Initial Layers and Uniqueness of¶Weak Entropy Solutions to¶Hyperbolic Conservation Laws

2000 ◽  
Vol 153 (3) ◽  
pp. 205-220 ◽  
Author(s):  
Gui-Qiang Chen ◽  
Michel Rascle
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Entropy Solutions ◽  
Hyperbolic Conservation ◽  
Initial Layers

scholarly journals On Approximation of Entropy Solutions for One System of Nonlinear Hyperbolic Conservation Laws with Impulse Source Terms

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Ciro D'Apice ◽  
Peter I. Kogut ◽  
Rosanna Manzo
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Dynamic Models ◽  
Optimization Problems ◽  
Fluid Dynamic ◽  
Entropy Solutions ◽  
Source Terms ◽  
Hyperbolic Conservation ◽  
Linear Evolution ◽  
Linear Evolution Equation

We study one class of nonlinear fluid dynamic models with impulse source terms. The model consists of a system of two hyperbolic conservation laws: a nonlinear conservation law for the goods density and a linear evolution equation for the processing rate. We consider the case when influx-rates in the second equation take the form of impulse functions. Using the vanishing viscosity method and the so-called principle of fictitious controls, we show that entropy solutions to the original Cauchy problem can be approximated by optimal solutions of special optimization problems.

scholarly journals On the structure of BV entropy solutions for hyperbolic systems of balance laws with general flux function

2019 ◽  
Vol 16 (02) ◽  
pp. 333-378
Author(s):  
Fabio Ancona ◽  
Laura Caravenna ◽  
Andrea Marson
Keyword(s):  
Conservation Laws ◽  
Wave Front ◽  
Hyperbolic System ◽  
Hyperbolic Conservation Laws ◽  
Hyperbolic Systems ◽  
Entropy Solutions ◽  
Balance Laws ◽  
Hyperbolic Conservation ◽  
Flux Function ◽  
Systems Of Balance Laws

The paper describes the qualitative structure of BV entropy solutions of a general strictly hyperbolic system of balance laws with characteristic field either piecewise genuinely nonlinear or linearly degenerate. In particular, we provide an accurate description of the local and global wave-front structure of a BV solution generated by a fractional step scheme combined with a wave-front tracking algorithm. This extends the corresponding results in [S. Bianchini and L. Yu, Global structure of admissible BV solutions to piecewise genuinely nonlinear, strictly hyperbolic conservation laws in one space dimension, Comm. Partial Differential Equations 39(2) (2014) 244–273] for strictly hyperbolic system of conservation laws.

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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