A general BV existence result for conservation laws with spatial heterogeneities.

*(English)*Zbl 1402.35171The authors study entropy solutions to the 1-D scalar conservation law \(\frac{\partial\rho}{\partial t}+\frac{\partial}{\partial x} A(\rho,x)=0\), where the flux function \(A(\rho,x)\) may be discontinuous with respect to the spatial variable. Under some additional structural assumptions on the flux the authors prove the existence of an adapted entropy solution in the sense of E. Audusse and B. Perthame [Proc. R. Soc. Edinb., Sect. A, Math. 135, No. 2, 253–266 (2005; Zbl 1071.35079)] in the BV framework.

Reviewer: Evgeniy Panov (Novgorod)

##### MSC:

35L65 | Hyperbolic conservation laws |

35A01 | Existence problems for PDEs: global existence, local existence, non-existence |

35B44 | Blow-up in context of PDEs |

35D30 | Weak solutions to PDEs |

35L03 | Initial value problems for first-order hyperbolic equations |

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\textit{B. Piccoli} and \textit{M. Tournus}, SIAM J. Math. Anal. 50, No. 3, 2901--2927 (2018; Zbl 1402.35171)

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