Resonance for the isothermal system of isentropic gas dynamics
Author:
Yunguang Lu
Journal:
Proc. Amer. Math. Soc. 139 (2011), 28212826
MSC (2010):
Primary 35L65, 76N10
Published electronically:
February 8, 2011
MathSciNet review:
2801623
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Abstract 
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Additional Information
Abstract: In this paper, we remove the restriction or in the paper ``Existence of Solutions to Hyperbolic Conservation Laws with a Source'' (Commun. Math. Phys., 187 (1997), 327340) and obtain the existence of solutions for the resonant, isothermal system of isentropic gas dynamics.
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 J. Glimm, Solutions in the large for nonlinear hyperbolic systems of equations, Comm. Pure Appl. Math., 18 (1965), 95105. MR 0194770 (33:2976)
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 J. Glimm, G. Marshall and B. Plohr, A generalized Riemann problem for quasionedimensional gas flows, Adv. Appl. Math., 5 (1984), 130. MR 736548 (85e:76041)
 [HW]
 F.M Huang and Z. Wang, Convergence of viscosity solutions for isentropic gas dynamics, SIAM J. Math. Anal., 34 (2003), 595610. (1984), 130.
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 E. Isaacson and B. Temple, Nonlinear resonance in systems of conservation laws, SIAM J. Appl. Math., 52 (1992), 12601278. MR 1182123 (93f:35140)
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 C. Klingenberg and Y.G. Lu, Existence of solutions to hyperbolic conservation laws with a source, Commun. Math. Phys., 187 (1997), 327340. MR 1463831 (98d:35139)
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 T.P. Liu, Resonance for a quasilinear hyperbolic equation, J. Math. Phys., 28 (1987), 25932602. MR 913412 (88k:35122)
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 Y.G. Lu, Hyperbolic Conservation Laws and the Compensated Compactness Method, Vol. 128, Chapman and Hall, CRC Press, New York, 2002.
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Additional Information
Yunguang Lu
Affiliation:
Department of Mathematics, Hangzhou Normal University, Hangzhou, 310036, People’s Republic of China – and – Department of Mathematics, National University of Colombia, Bogota, Colombia
Email:
yglu_2000@yahoo.com
DOI:
http://dx.doi.org/10.1090/S000299392011107330
Keywords:
Resonance,
gas dynamics,
global weak solution,
$L^{\infty}$ estimate
Received by editor(s):
April 6, 2010
Received by editor(s) in revised form:
April 27, 2010, and July 26, 2010
Published electronically:
February 8, 2011
Additional Notes:
The author thanks the referee for many valuable suggestions.
Communicated by:
Matthew J. Gursky
Article copyright:
© Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
