On the stability of the standard Riemann semigroup
Authors:
Stefano Bianchini and Rinaldo M. Colombo
Journal:
Proc. Amer. Math. Soc. 130 (2002), 19611973
MSC (2000):
Primary 35L65, 76N10
Published electronically:
February 27, 2002
MathSciNet review:
1896028
Fulltext PDF Free Access
Abstract 
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Abstract: We consider the dependence of the entropic solution of a hyperbolic system of conservation laws
on the flux function . We prove that the solution is Lipschitz continuous w.r.t. the norm of the derivative of the perturbation of . We apply this result to prove the convergence of the solution of the relativistic Euler equation to the classical limit.
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 F. Ancona, A. Marson, Well posedness for general systems of conservation laws, preprint.
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 P. Baiti, A. Bressan, The semigroup generated by a Temple class system with large data, Differential Integral Equations 10 (1997), no. 3, p. 401418. MR 2000k:35180
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 S. Bianchini, On the shift differentiability of the flow generated by a hyperbolic system of conservation laws, Discr. Cont. Dyn. Sys. 62 (2000), pag. 329350. MR 2000m:35120
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 A. Bressan, The unique limit of the Glimm scheme, Arch. Rat. Mech. Anal. 130 (1995), 205230. MR 96d:65143
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 A. Bressan, ``Hyperbolic Systems of Conservation Laws: the One Dimensional Cauchy Problem'', Oxford Univ. Press (2000).
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 A. Bressan, G. Crasta, B. Piccoli, Well posedness of the Cauchy problem for systems of conservation laws, Mem. Amer. Math. Soc. 694 (2000). MR 2000m:35122
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 A.I. Panasyuk, Quasidifferential equations in a metric space, Differentsialnye Uravneniya, 21 (1985), no 8. MR 87b:34078
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 J. Smoller, B. Temple, Global Solutions of the Relativistic Euler Equations, Comm. Math. Phys. 156 (1993), 6799. MR 94h:35216
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Additional Information
Stefano Bianchini
Affiliation:
Istituto per le Applicazioni del Calcolo, Viale del Policlinico 137, 00161 Roma, Italy
Email:
bianchin@iac.rm.cnr.it
Rinaldo M. Colombo
Affiliation:
Department of Mathematics, University of Brescia, Via Valotti 9, 25133 Brescia, Italy
Email:
rinaldo@ing.unibs.it
DOI:
http://dx.doi.org/10.1090/S0002993902065681
PII:
S 00029939(02)065681
Keywords:
Hyperbolic systems,
conservation laws,
well posedness
Received by editor(s):
July 1, 2000
Published electronically:
February 27, 2002
Additional Notes:
We thank Alberto Bressan for useful discussions.
Communicated by:
Suncica Canic
Article copyright:
© Copyright 2002
American Mathematical Society
