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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