Entropy type conditions for Riemann solvers at nodes

Details Entropy type conditions for Riemann solvers at nodes Entropy type conditions for Riemann solvers at nodes

2009-05-27

arxiv.org/abs/0905.4408v1

Mathematics

Analysis of PDEs

35 pages

Scientific paper

This paper deals with conservation laws on networks, represented by graphs. Entropy-type conditions are considered to determine dynamics at nodes. Since entropy dispersion is a local concept, we consider a network composed by a single node $J$ with $n$ incoming and $m$ outgoing arcs. We extend at $J$ the classical Kru\v{z}kov entropy obtaining two conditions, denoted by (E1) and (E2): the first requiring entropy condition for all Kru\v{z}kov entropies, the second only for the value corresponding to sonic point. First we show that in case $n \ne m$, no Riemann solver can satisfy the strongest condition. Then we characterize all the Riemann solvers at $J$ satisfying the strongest condition (E1), in the case of nodes with at most two incoming and two outgoing arcs. Finally we focus three different Riemann solvers, introduced in previous papers. In particular, we show that the Riemann solver introduced for data networks is the only one always satisfying (E2).

Affiliated with

Also associated with

No associations

Rating

Entropy type conditions for Riemann solvers at nodes does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Entropy type conditions for Riemann solvers at nodes, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Entropy type conditions for Riemann solvers at nodes will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-527684