New entropy conditions for scalar conservation laws with discontinuous flux
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In this paper, the authors proposed new Kruzhkov type entropy conditions for one dimensional conservation law with a discontinuous flux, and proved the existence and uniqueness of the entropy admissible weak solution to the corresponding Cauchy problem.Abstract:
We propose new Kruzhkov type entropy conditions for one dimensional
scalar conservation law with a discontinuous flux. We prove
existence and uniqueness of the entropy admissible weak solution to
the corresponding Cauchy problem merely under assumptions on the
flux which provide the maximum principle. In particular, we allow
multiple flux crossings and we do not need any kind of genuine
nonlinearity conditions.read more
Citations
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Entropy conditions for scalar conservation laws with discontinuous flux revisited
TL;DR: In this paper, the authors proposed new entropy admissibility conditions for multidimensional hyperbolic scalar conservation laws with discontinuous flux which generalize one-dimensional Karlsen-Risebro-Towers entropy conditions.
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On interface transmission conditions for conservation laws with discontinuous flux of general shape
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TL;DR: In this paper, the authors introduce and exploit the idea of transmission maps for the interface condition at the discontinuity, leading to the well-posedness for the Cauchy problem with general shape of fl, r. The design and convergence of monotone Finite Volume schemes based on one-sided approximate Riemann solvers are then assessed.
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Convergence of a Godunov scheme for conservation laws with a discontinuous flux lacking the crossing condition
TL;DR: In this article, a scalar conservation law whose flux has a single spatial discontinuity is studied, and the authors focus on the notion of entropy solution, the relevant concept being determined by the application.
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Structure of Solutions of Multidimensional Conservation Laws with Discontinuous Flux and Applications to Uniqueness
TL;DR: In this article, the authors investigated the structure of solutions of conservation laws with discontinuous flux under quite general assumption on the flux and showed that any entropy solution admits traces on the discontinuity set of the coefficients and used this to prove the validity of a generalized Kato inequality for any pair of solutions.
References
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Microlocal defect measures
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