A kinetic formulation for multi-branch entropy solutions of scalar conservation laws

Abstract

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Multi-Water-Bag Model And Method Of Moments For The Vlasov Equation

“…In Section 4, we compare numerically the two kinds of solutions. It is also possible to compute several branches by the method of moments [4].…”

“…In general, the system may have several solutions. Uniqueness can be recovered through an entropy argument [4].…”

“…where −∞ < a 2N ≤ · · · ≤ a 1 < +∞, we can use the algorithm described in [4,7], which solves rigorously such a system. It is then possible to catch numerically the multivalued solutions.…”

Multiphase semiclassical approximation of the one-dimensional harmonic crystal: I. The periodic case

“…This method has been originally introduced in [9,22] following the seminal work by Brenier and Corrias [6]. Is is based on the remark that geometrical solutions to (7)- (9) can be recovered from the solving of a rather simple system of nonlinear conservation laws through the moment closure of a kinetic equation.…”

“…A remarkable feature is that (11) can be obtained from an entropy minimization process; this eventually led to the definition of K-multivalued solutions in [6]:…”