scholarly journals Convergence of a Godunov scheme to an Audusse–Perthame adapted entropy solution for conservation laws with BV spatial flux

2020 ◽  
Vol 146 (3) ◽  
pp. 629-659
Author(s):  
Shyam Sundar Ghoshal ◽  
Animesh Jana ◽  
John D. Towers
Keyword(s):  
Conservation Laws ◽  
Entropy Solution ◽  
Godunov Scheme

scholarly journals A Bhatnagar–Gross–Krook approximation to scalar conservation laws with discontinuous flux

2010 ◽  
Vol 140 (5) ◽  
pp. 953-972 ◽  
Author(s):  
F. Berthelin ◽  
J. Vovelle
Keyword(s):  
Conservation Laws ◽  
Entropy Solution ◽  
Limit Problem ◽  
Scalar Conservation Laws ◽  
First Order ◽  
The Cauchy Problem ◽  
Discontinuous Flux ◽  
Scalar Conservation ◽  
Bgk Approximation ◽  
Well Posed

AbstractWe study the Bhatnagar–Gross–Krook (BGK) approximation to first-order scalar conservation laws with a flux which is discontinuous in the space variable. We show that the Cauchy problem for the BGK approximation is well posed and that, as the relaxation parameter tends to 0, it converges to the (entropy) solution of the limit problem.

ABOUT UNIQUENESS OF WEAK SOLUTIONS TO FIRST ORDER QUASI-LINEAR EQUATIONS

2002 ◽  
Vol 12 (11) ◽  
pp. 1599-1615 ◽  
Author(s):  
J. NIETO ◽  
J. SOLER ◽  
F. POUPAUD
Keyword(s):  
Conservation Laws ◽  
Weak Solutions ◽  
Entropy Solution ◽  
Linear Equations ◽  
Particle Method ◽  
Entropy Condition ◽  
First Order

In this paper we give a criterion to discriminate the entropy solution to quasi-linear equations of first order among weak solutions. This uniqueness statement is a generalization of Oleinik's criterion, which makes reference to the measure of the increasing character of weak solutions. The link between Oleinik's criterion and the entropy condition due to Kruzhkov is also clarified. An application of this analysis to the convergence of the particle method for conservation laws is also given by using the Filippov characteristics.

scholarly journals Conservation laws driven by Lévy white noise

2015 ◽  
Vol 12 (03) ◽  
pp. 581-654 ◽  
Author(s):  
Imran H. Biswas ◽  
Kenneth H. Karlsen ◽  
Ananta K. Majee
Keyword(s):  
Conservation Laws ◽  
Entropy Solution ◽  
Young Measure ◽  
Entropy Solutions ◽  
Contraction Principle ◽  
Viscosity Method ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Lévy White Noise ◽  
Entropy Inequalities

We consider multidimensional conservation laws perturbed by multiplicative Lévy noise. We establish existence and uniqueness results for entropy solutions. The entropy inequalities are formally obtained by the Itó–Lévy chain rule. The multidimensionality requires a generalized interpretation of the entropy inequalities to accommodate Young measure-valued solutions. We first prove the existence of entropy solutions in the generalized sense via the vanishing viscosity method, and then establish the L1-contraction principle. Finally, the L1 contraction principle is used to argue that the generalized entropy solution is indeed the classical entropy solution.

A BOUNDED VARIATION ESTIMATE FOR THE FORCE SCHEME APPLIED TO STRICTLY HYPERBOLIC SYSTEMS OF CONSERVATION LAWS IN THE TEMPLE CLASS

2013 ◽  
Vol 10 (01) ◽  
pp. 105-127
Author(s):  
RAJIB DUTTA
Keyword(s):  
Probability Theory ◽  
Initial Data ◽  
Conservation Laws ◽  
Random Walks ◽  
Total Variation ◽  
Bounded Variation ◽  
Hyperbolic Systems ◽  
Godunov Scheme ◽  
Systems Of Conservation Laws ◽  
The Temple

Bressan and Jenssen established a uniform bounded variation (BV) estimate for the Godunov scheme for Temple-type strictly hyperbolic systems of conservation laws and gave a proof based on the probability theory of random walks. In this paper, we provide a different proof which is simpler and does not use any probability theory. Applying our theory, we establish a uniform BV estimate for the Force scheme for the same class of hyperbolic systems, under the assumption of small total variation of initial data.

Sign in / Sign up

Export Citation Format

Share Document