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

Darko Mitrovic; Ivan Ivec

doi:10.3934/cpaa.2011.10.1617

Article Contents

2011, Volume 10, Issue 6: 1617-1627. Doi: 10.3934/cpaa.2011.10.1617

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

Darko Mitrovic^1, and
Ivan Ivec^2,

1.
Faculty of Mathematics, University of Montenegro, Cetinjski put bb, 81000 Podgorica
2.
Faculty of Mathematics, University of Zagreb, Bijenicka cesta 30, 10000 Zagreb

Received: December 31, 2009

Revised: February 28, 2011

Published: October 2011

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Abstract

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.

Keywords:

$H$-measures,
fractional conservation laws.

Mathematics Subject Classification: Primary: 35L99, 35L65; Secondary: 42B15.

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References

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