Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 
 

 

Von Neumann's comments about existence and uniqueness for the initial-boundary value problem in gas dynamics


Author: Denis Serre
Journal: Bull. Amer. Math. Soc. 47 (2010), 139-144
MSC (2010): Primary 01A60, 35L65, 35L67, 35Q35, 35Q85, 76N10, 76N15, 76P05, 85A30
DOI: https://doi.org/10.1090/S0273-0979-09-01286-5
Published electronically: October 15, 2009
MathSciNet review: 2566448
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • 1. A. Bressan. Hyperbolic systems of conservation laws. Oxford Lecture Series in Mathematics and its Applications, 20. Oxford University Press, Oxford (2000). MR 1816648 (2002d:35002)
  • 2. G.-Q. Chen and M. Feldman. Potential theory for shock reflection by a large-angle wedge. Proc. Nat. Acad. Sci. USA, 102 (2005), pp. 15368-15372. MR 2188921 (2006f:35214)
  • 3. R. J. DiPerna. Convergence of the viscosity method for isentropic gas dynamics. Comm. Math. Phys., 91 (1983) pp. 1-30. Convergence of approximate solutions to conservation laws. Arch. Rat. Mech. Anal., 82 (1983), pp. 27-70. MR 719807 (85i:35118)
  • 4. J. Glimm. Solutions in the large for nonlinear hyperbolic systems of equations. Comm. Pure Appl. Math., 18 (1965), pp. 697-715. MR 0194770 (33:2976)
  • 5. S. Kruzkov. Generalized solutions of the Cauchy problem in the large for nonlinear equations of first order. Dokl. Akad. Nauk SSSR, 187 (1969), pp. 29-32. MR 0249805 (40:3046)
  • 6. P. D. Lax. Hyperbolic systems of conservation laws (II). Comm. Pure Appl. Math., 10 (1957), pp. 537-566. MR 0093653 (20:176)
  • 7. J. Rauch. BV estimates fail for most quasilinear hyperbolic systems in dimensions greater than one. Comm. Math. Phys., 106 (1986), pp. 481-484. MR 859822 (87m:35139)

Similar Articles

Retrieve articles in Bulletin of the American Mathematical Society with MSC (2010): 01A60, 35L65, 35L67, 35Q35, 35Q85, 76N10, 76N15, 76P05, 85A30

Retrieve articles in all journals with MSC (2010): 01A60, 35L65, 35L67, 35Q35, 35Q85, 76N10, 76N15, 76P05, 85A30


Additional Information

Denis Serre
Affiliation: École Normale Supérieure de Lyon, D. S.: UMPA, CNRS UMR 5669. ENS de Lyon, 46 allée d’Italie. F-69364 Lyon, cedex 07, France

DOI: https://doi.org/10.1090/S0273-0979-09-01286-5
Received by editor(s): September 8, 2009
Published electronically: October 15, 2009
Article copyright: © Copyright 2009 American Mathematical Society

American Mathematical Society