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

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  • 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 $L_{l o c}^1$ precompactness of such quasi-solutions.
    Mathematics Subject Classification: Primary: 35L99, 35L65; Secondary: 42B15.


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