Regularizing effects for multidimensional scalar conservation laws
type: Item
instance of: scholarly article
title: Regularizing effects for multidimensional scalar conservation laws
zbMATH Open document ID: 0966.35074
DOI: 10.1016/S0294-1449(00)00116-5
published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire
publication date: 2001-08-07T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/78497
review text: It has been known for a long time that multidimensional scalar conservation laws possess a unique weak entropy solution in \(L^1\cap L^{\infty}\) which however need not be of bounded variation. The present paper deals with the important question whether the nonlinearity of the flux acts as a regularizing effect. For a flux which in each direction is either strictly convex or possesses at most one nondegenerate inflection point, the author is able to derive estimates for some quantity \(\Theta\) that is obtained via a scattering procedure. These estimates are sufficient to derive a number of interesting conclusions, e.g. BV- and Sobolev estimates for some averaged quantities or decay estimates for spatially periodic solutions.
reviewed by: Jörg Härterich
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35L45
zbMATH DE Number: 1546941
zbMATH Keywords: BV- and Sobolev estimates for some averaged quantities
zbMATH Keywords: kinetic formulation
zbMATH Keywords: entropy solutions
zbMATH Keywords: scattering
zbMATH Keywords: Radon transform
zbMATH Keywords: two-microlocal regularity
zbMATH Keywords: decay estimates for spatially periodic solutions
author: Christophe Cheverry
MaRDI profile type: Publication
cites work: Q3220998
cites work: Averaging lemmas without time Fourier transform and application to discretized kinetic equations
cites work: Hypoelliptic regularity in kinetic equations.
cites work: Averaged Multivalued Solutions for Scalar Conservation Laws
cites work: The formation and decay of shocks for a conservation law in several dimensions
cites work: Q3915362
cites work: Regularity and large time behaviour of solutions of a conservation law without convexity
cites work: \(L^ p\) regularity of velocity averages
cites work: Large time behavior and homogenization of solutions of two‐dimensional conservation laws
cites work: Moyennisation et régularité deux-microlocale
cites work: Regularity of the moments of the solution of a transport equation
cites work: The Radon transform
cites work: Q3844581
cites work: The Formation and Decay of Shock Waves
cites work: A Kinetic Formulation of Multidimensional Scalar Conservation Laws and Related Equations
cites work: Hyperbolic systems of conservation laws II
cites work: A Poincaré–Bendixson theorem for scalar balance laws
cites work: Q4183803
cites work: Discontinuous solutions of non-linear differential equations
cites work: A regularizing effect of nonlinear transport equations
cites work: A kinetic equation with kinetic entropy functions for scalar conservation laws
cites work: A regularity theorem for conservation laws
cites work: Q3049266
cites work: THE SPACES $ BV$ AND QUASILINEAR EQUATIONS
cites work: Decay rates for nonconvex systems of conservation laws
OpenAlex ID: W1989462402
Recommended article: Q5301256
Recommended article: Optimal regularizing effect for scalar conservation laws
Recommended article: Q5188109
Recommended article: Regularizing effect for conservation laws with a Lipschitz convex flux
Recommended article: Hyperbolic regularizations of conservation laws
Recommended article: Q4444860
Recommended article: Q4831647
Recommended article: The regularized Chapman-Enskog expansion for scalar conservation laws
Recommended article: On a regularization of a scalar conservation law with discontinuous coefficients
Recommended article: Q3074322
description: scientific article; zbMATH DE number 1546941