scholarly journals GENERALIZED MULTI-POLYTROPIC RANKINE–HUGONIOT RELATIONS AND THE ENTROPY CONDITION

2016 ◽  
Vol 833 (1) ◽  
pp. 38 ◽  
Author(s):  
Klaus Scherer ◽  
Horst Fichtner ◽  
Hans Jörg Fahr ◽  
Christian Röken ◽  
Jens Kleimann
Keyword(s):  
Entropy Condition

Uniqueness of the regular waiting-time type solution of the thin film equation

2012 ◽  
Vol 23 (4) ◽  
pp. 537-554 ◽  
Author(s):  
MARINA CHUGUNOVA ◽  
JOHN R. KING ◽  
ROMAN M. TARANETS
Keyword(s):  
Thin Film ◽  
Initial Data ◽  
Waiting Time ◽  
Entropy Condition ◽  
Type Solution ◽  
Energy Equality ◽  
Thin Film Equation ◽  
Gronwall’S Lemma ◽  
Touchdown Point ◽  
Time Type

The main result of this paper is the proof of uniqueness of non-negative entropy solutions of the thin film equation ht + (|h|nhxxx)x = 0 for $\frac{7}{4}$ < n < 4. The uniqueness proved under assumptions that the initial data satisfy a finite β-entropy condition for some negative enough exponent β and that the solution is locally monotone at the touchdown point. The new dissipated functional recently constructed by Laugesen (Commun. Pure Appl. Anal., 4(3):613–634, 2005) is used to prove an auxiliary energy equality, and then Grönwall's lemma leads to uniqueness.

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.

On the local fractional LWR model in fractal traffic flows in the entropy condition

2015 ◽  
Vol 40 (17) ◽  
pp. 6127-6132 ◽  
Author(s):  
Yong-Mei Guo ◽  
Yang Zhao ◽  
Yao-Ming Zhou ◽  
Zhong-Bin Xiao ◽  
Xiao-Jun Yang
Keyword(s):  
Traffic Flows ◽  
Entropy Condition ◽  
Lwr Model
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