Hyperbolic exterior differential systems and their conservation laws, part II
@article{Bryant1995HyperbolicED,
title={Hyperbolic exterior differential systems and their conservation laws, part II},
author={Robert L. Bryant and Phillip A. Griffiths and Lucas Hsu},
journal={Selecta Mathematica},
year={1995},
volume={1},
pages={265-323},
url={https://api.semanticscholar.org/CorpusID:15812302}
}This research was supported in part by NSF Grant DMS 9205222 (Bryant), an NSERC Postdoctoral Fellowship (Hsu), and the Institute for Advanced Study (Griffiths and Hsu).IAS Preprint: 1/25/94.
Part II will appear in Vol. 1, No. 2 of this journal.
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22 References
Uniqueness via the adjoint problems for systems of conservation laws
- 1993
Mathematics
We prove a result of uniqueness of the entropy weak solution to the Cauchy problem for a class of nonlinear hyperbolic systems of conservation laws that includes in particular the p-system of…
Development of Singularities of Solutions of Nonlinear Hyperbolic Partial Differential Equations
- 1964
Mathematics
In a recent paper Zabusky has given an accurate estimate of the time interval in which solutions of the nonlinear string equation ytt = c2(1 + eyx)yxx exist. A previous numerical study of solutions…
A fundamental property of Monge characteristics in involutive systems of non-linear partial differential equations and its application
- 1985
Mathematics
On eclaircit un nouvel aspect de la notion de caracteristiques de Monge. On deduit un theoreme d'existence de solutions infiniment differentiables pour des systemes involutifs dont les caracteres de…
Methods of mathematical physics, Volume I
- 1965
Mathematics
2008; John Wiley & Sons, 2008; Methods of Mathematical Physics, Volume 1; 575 pages; 3527617221, 9783527617227; Richard Courant, D. Hilbert; Since the first volume of this work came out in Germany in…