Stochastic conservation laws: Weak-in-time formulation and strong entropy condition

On weak convergence of entropy solutions to scalar conservation laws

We prove that weak limits of entropy solutions to a one-dimensional scalar conservation law are entropy solutions as well. We consider a scalar conservation law ut + f(u)x = 0, (t, x) ∈ Π = (0, +∞)× R. (1) The flux function f(u) is supposed to be only continuous: f(u) ∈ C(R). Recall the notion of an entropy solution of (1) in the sense of Kruzhkov [6]. Definition 1. A bounded measurable functio...

Stochastic Conservation Laws?

We examine conservation laws, typically the conservation of linear momentum, in the light of a recent successful formulation of fermions as Kerr-Newman type Black Holes, which are created uctuationally from a background Zero Point Field. We conclude that these conservation laws are to be taken in the spirit of thermodynamic laws. Conservation Laws, as is universally known, play an important rol...

Large-time Behavior of Entropy Solutions of Conservation Laws

We are concerned with the large-time behavior of discontinuous entropy solutions for hyperbolic systems of conservation laws. We present two analytical approaches and explore their applications to the asymptotic problems for discontinuous entropy solutions. These approaches allow the solutions of arbitrarily large oscillation without apriori assumption on the ways from which the solutions come....

Strong, Weak and False Inverse Power Laws

Pareto, Zipf and numerous subsequent investigators of inverse power distributions have often represented their findings as though their data conformed to a power law form for all ranges of the variable of interest. I refer to this ideal case as a strong inverse power law (SIPL). However, many of the examples used by Pareto and Zipf, as well as others who have followed them, have been truncated ...

L2 formulation of multidimensional scalar conservation laws