How parabolic free boundaries approximate hyperbolic fronts

A rather complete study of the existence and qualitative behaviour of the boundaries of the support of solutions of the Cauchy problem for nonlinear first-order and second-order scalar conservation laws is presented. Among other properties, it is shown that, under appropriate assumptions, parabolic...

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Bibliographic Details
Published in:Transactions of the American Mathematical Society 2000-04, Vol.352 (4), p.1797-1824
Main Authors: Gilding, Brian H., Natalini, Roberto, Tesei, Alberto
Format: Article
Language:English
Subjects:
Cauchy problem
Conservation laws
Entropy
Equations
Mathematical functions
Mathematical theorems
Mathematics
Porous materials
Shock waves
Viscosity
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Summary:A rather complete study of the existence and qualitative behaviour of the boundaries of the support of solutions of the Cauchy problem for nonlinear first-order and second-order scalar conservation laws is presented. Among other properties, it is shown that, under appropriate assumptions, parabolic interfaces converge to hyperbolic ones in the vanishing viscosity limit.
ISSN:0002-9947
1088-6850
DOI:10.1090/S0002-9947-99-02236-9