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

2011/03/06 by Mitrovic, Darko, Ivec, Ivan
#35L65 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary: 35L99 #Secondary: 42B15

paper · doi:10.48550/arxiv.1103.1108

Abstract

We extend the notion of H-measures on test functions defined on \R^d× P, where P⊂ \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 L¹_loc precompactness of such quasi-solutions.

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