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Journal Articles SIAM Journal on Mathematical Analysis Year : 2018

A general BV existence result for conservation laws with spatial heterogeneities

Abstract

We consider a scalar conservation law with a flux containing spatial heterogeneities of bounded variation, where the number of discontinuities may be infinite. We prove existence of an adapted entropy solution in the sense of Audusse-Perthame in the BV framework, under the assump- tions that guarantee uniqueness of the solution, plus one additional technical assumption. We prove that existence in the BV framework fails withouth this additional technical assumption, by providing a counter-example.
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Dates and versions

hal-01352538 , version 1 (08-08-2016)
hal-01352538 , version 2 (06-04-2017)
hal-01352538 , version 3 (06-04-2018)

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Cite

Benedetto Piccoli, Magali Tournus. A general BV existence result for conservation laws with spatial heterogeneities. SIAM Journal on Mathematical Analysis, 2018, 50 (3), pp.2901-2927. ⟨10.1137/17M112628X⟩. ⟨hal-01352538v3⟩
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