A Minimality Property for Entropic Solutions to Scalar Conservation Laws in 1 + 1 Dimensions

Details A Minimality Property for Entropic Solutions to Scalar Conservation Laws in 1 + 1 Dimensions A Minimality Property for Entropic Solutions to Scalar Conservation Laws in 1 + 1 Dimensions

2009-07-24

arxiv.org/abs/0907.4215v1

Mathematics

Analysis of PDEs

43 pages

Scientific paper

The Second Law of Thermodynamics asserts that the physical entropy of an adiabatic system is an increasing function in time. In this paper we will study a more stringent version of this law, according to which the entropy should not only increase in time, but the rate of increase is optimal in absolute value among all possible evolutions. We will establish this property in the framework of non-linear scalar hyperbolic conservation law with strictly convex fluxes.

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