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Uniqueness for a Scalar Conservation Law with Discontinuous Flux via Adapted Entropies

机译:通过自适应熵实现具有不连续通量的标量守恒律的唯一性

摘要

We prove uniqueness of solutions to scalar conservation laws with space discontinuous fluxes. To do so, we introduce a partial adaptation of Kruzkov's entropies which naturally takes into account the space dependency of the flux. The advantage of this approach is that the proof turns out to be a simple variant of Kruzkov's original method. Especially, we do not need traces, interface condition, Bounded Variation assumptions (neither on the solution nor on the flux), or convex fluxes. However we use a special 'local uniform invertibility' structure of the flux which applies to cases where different interface condiftions are known to yield different solutions.
机译:我们证明了具有空间不连续通量的标量守恒定律的解的唯一性。为此,我们引入了对克鲁兹科夫熵的部分适应,这自然考虑了通量的空间依赖性。这种方法的优势在于证明是克鲁兹科夫原始方法的简单变体。特别是,我们不需要迹线,界面条件,有界变化假设(既不在解决方案上,也不在通量上)或凸通量。但是,我们使用了一种特殊的通量“局部均匀可逆性”结构,该结构适用于已知不同界面条件产生不同解的情况。

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