Fractional BV spaces and applications to scalar conservation laws

被引：19

作者：

Bourdarias, C. ^{[1
]}

Gisclon, M. ^{[1
]}

Junca, S. ^{[2
,3
]}

机构：

[1] Univ Savoie, LAMA, CNRS, UMR 5127, F-73376 Le Bourget Du Lac, France

[2] Univ Nice Sophia Antipolis, UMR CNRS 7351, Labo JAD, F-06189 Nice, France

[3] INRIA Sophia Antipolis Mediterannee, Team COFFE, F-06902 Sophia Antipolis, France

来源：

JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS | 2014年 / 11卷 / 04期

关键词：

Generalized bounded variation; nonlinear convex flux; conservation law; entropy solution; regularity theory; WAVES;

D O I：

10.1142/S0219891614500209

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We obtain new fine properties of entropy solutions to scalar nonlinear conservation laws. For this purpose, we study the "fractional BV spaces" denoted by BVs(R) (for 0 < s <= 1), which were introduced by Love and Young in 1937 and closely related to the critical Sobolev space W-s,W-1/s(R). We investigate these spaces in connection with one-dimensional scalar conservation laws. The BVs spaces allow one to work with less regular functions than BV functions and appear to be more natural in this context. We obtain a stability result for entropy solutions with BVs initial data. Furthermore, for the first time, we get the maximal W-s,W-p smoothing effect conjectured by Lions, Perthame and Tadmor for all nonlinear (possibly degenerate) convex fluxes.

引用

页码：655 / 677

页数：23

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