BV regularity near the interface for nonuniform convex discontinuous flux

Shyam Sundar  Ghoshal; Shyam Sundar  Ghoshal

doi:10.3934/nhm.2016.11.331

Networks and Heterogeneous Media

2016, Volume 11, Issue 2: 331-348. doi: 10.3934/nhm.2016.11.331

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BV regularity near the interface for nonuniform convex discontinuous flux

Shyam Sundar Ghoshal ^{1
,}

1.
Gran Sasso Science Institute, Viale Francesco Crispi, 7, 67100 LAquila

Received: 01 April 2015 Revised: 01 September 2015
Primary: 35B65, 35L65, 35L67.

In this paper, we discuss the total variation bound for the solution of scalar conservation laws with discontinuous flux. We prove the smoothing effect of the equation forcing the $BV_{loc}$ solution near the interface for $L^\infty$ initial data without the assumption on the uniform convexity of the fluxes made as in [1,21]. The proof relies on the method of characteristics and the explicit formulas.
- Hamilton-Jacobi equation,
- conservation laws,
- discontinuous flux,
- explicit formula,
- characteristics,
- BV function
Citation: Shyam Sundar Ghoshal. BV regularity near the interface for nonuniform convex discontinuous flux[J]. Networks and Heterogeneous Media, 2016, 11(2): 331-348. doi: 10.3934/nhm.2016.11.331

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Abstract

In this paper, we discuss the total variation bound for the solution of scalar conservation laws with discontinuous flux. We prove the smoothing effect of the equation forcing the $BV_{loc}$ solution near the interface for $L^\infty$ initial data without the assumption on the uniform convexity of the fluxes made as in [1,21]. The proof relies on the method of characteristics and the explicit formulas.

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