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A general BV existence result for conservation laws with spatial heterogeneities. (English) Zbl 1402.35171
The 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.

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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