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BV regularity near the interface for nonuniform convex discontinuous flux. (English) Zbl 1343.35050
Summary: 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 $$BV_{\mathrm{loc}}$$ solution near the interface for $$L^\infty$$ initial data without the assumption on the uniform convexity of the fluxes made as in [Adimurthi et al., Commun. Pure Appl. Math. 64, No. 1, 84–115 (2011; Zbl 1223.35222); the author, J. Differ. Equations 258, No. 3, 980–1014 (2015; Zbl 1312.35032)]. The proof relies on the method of characteristics and the explicit formulas.

##### MSC:
 35B65 Smoothness and regularity of solutions to PDEs 35L65 Hyperbolic conservation laws 35L67 Shocks and singularities for hyperbolic equations 35F21 Hamilton-Jacobi equations
##### Keywords:
explicit formula; characteristics; smoothing effect
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