A generalization of $H$-measures and application on purely fractional scalar conservation laws

Details A generalization of $H$-measures and application on purely fractional scalar conservation laws A generalization of $H$-measures and application on purely fractional scalar conservation laws

2011-03-06

arxiv.org/abs/1103.1108v1

Mathematics

Analysis of PDEs

11 pages, 1 figure; to appear in CPAA

Scientific paper

We extend the notion of $H$-measures on test functions defined on $\R^d\times P$, where $P\subset \R^d$ is an arbitrary compact simply connected Lipschitz manifold such that there exists a family of regular nonintersecting curves issuing from the manifold and fibrating $\R^d$. We introduce a concept of quasi-solutions to purely fractional scalar conservation laws and apply our extension of the $H$-measures to prove strong $L^1_{loc}$ precompactness of such quasi-solutions.

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