scholarly journals Error estimators for the position of discontinuities in hyperbolic conservation laws with source terms which are solved using operator splitting

1999 ◽  
Vol 1 (4) ◽  
pp. 231-249 ◽  
Author(s):  
R. Jeltsch ◽  
P. Klingenstein
Keyword(s):  
Conservation Laws ◽  
Hyperbolic Conservation Laws ◽  
Operator Splitting ◽  
Source Terms ◽  
Hyperbolic Conservation ◽  
Error Estimators

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.

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