On the maximal smoothing effect for multidimensional scalar conservation laws. (May 2017)

• Record Type: Journal Article
• Authors: Castelli, Pierre; Junca, Stéphane
• Is Part Of: Nonlinear analysis. Volume 155(2017)
• Page Start: 207
• Page End: 218
• Publication Date: 2017-05
• Subjects: 35L65 -- 35B65 -- 35L67 -- 46E35 -- 26A45; Conservation laws -- Entropy solution -- Nonlinear flux -- Smoothing effect -- Generalized BV spaces; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2017.01.018
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In 1994, Lions, Perthame and Tadmor conjectured an optimal smoothing effect for entropy solutions of multidimensional scalar conservation laws. This effect estimated in fractional Sobolev spaces is linked to the flux nonlinearity. We use a new definition of a nonlinear smooth flux in order to show that the conjectured smoothing effect cannot be exceeded. First one-dimensional solutions are considered in fractional B V spaces. Then the multidimensional case is handled with a monophase solution.