Optimal Regularizing Effect for Scalar Conservation Laws
Fran\c{c}ois Golse, Beno\^it Perthame
TL;DR
This paper studies the regularity properties of solutions to scalar conservation laws with convex flux, using kinetic formulation and interaction estimates to understand entropy solutions with signed Radon measure entropy production.
Contribution
It introduces a novel approach combining kinetic formulation and interaction estimates to analyze regularity of entropy solutions with signed Radon measures.
Findings
Established regularity results for scalar conservation laws with convex flux.
Developed new interaction estimates in physical space.
Provided insights into entropy solutions with signed Radon measure entropy production.
Abstract
We investigate the regularity of bounded weak solutions of scalar conservation laws with uniformly convex flux in space dimension one, satisfying an entropy condition with entropy production term that is a signed Radon measure. The proof is based on the kinetic formulation of scalar conservation laws and on an interaction estimate in physical space.
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