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How parabolic free boundaries approximate hyperbolic fronts

Authors: Brian H. Gilding, Roberto Natalini and Alberto Tesei
Journal: Trans. Amer. Math. Soc. 352 (2000), 1797-1824
MSC (1991): Primary 35L65; Secondary 35K55, 35K65, 35L67, 35R35
Published electronically: November 18, 1999
MathSciNet review: 1487616
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Abstract: 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.

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Additional Information

Brian H. Gilding
Affiliation: Faculty of Applied Mathematics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands

Roberto Natalini
Affiliation: Istituto per le Applicazioni del Calcolo “M. Picone”, Consiglio Nazionale della Ricerche, Viale del Policlinico 137, I-00161 Roma, Italia

Alberto Tesei
Affiliation: Dipartimento di Matematica, Università degli Studi di Roma “La Sapienza”, Piazza A. Moro 5, I-00185 Roma, Italia

Keywords: Conservation law, convection-diffusion equation, degenerate parabolic problem, entropy solution, shock wave, finite speed of propagation, infinite speed of propagation, vanishing viscosity limit
Received by editor(s): June 17, 1996
Received by editor(s) in revised form: August 15, 1997
Published electronically: November 18, 1999
Article copyright: © Copyright 2000 American Mathematical Society

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