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Well-posed quasi-linear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity

Hughes , Thomas J. R. and Kato, Tosio and Marsden, Jerrold E. (1977) Well-posed quasi-linear second-order hyperbolic systems with applications to nonlinear elastodynamics and general relativity. Archive for Rational Mechanics and Analysis, 63 (3). pp. 273-294. ISSN 0003-9527. http://resolver.caltech.edu/CaltechAUTHORS:20100817-114853033

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Abstract

Existence, uniqueness and well-posedness for a general class of quasi-linear evolution equations on a short time interval are established. These results, generalizing those of [29], are applied to second-order quasi-linear hyperbolic systems on IR" whose solutions (u(t),il(t)) lie in the Sobolev space H^(s+1) x H^5. Our results improve existing theorems by lowering the required value of s to s > (n/2) + 1, or s > n/2 in case the coefficients of the highest order terms do not involve derivatives of the unknown, and by establishing continuous dependence on the initial data for these values. As consequences we obtain well-posedness of the equations of elastodynamics if s>2.5 and of general relativity if s>l.5; s>3 was the best known previous value for systems of the type occuring in general relativity ([12], [16], [23]).


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/BF00251584 DOIUNSPECIFIED
http://www.springerlink.com/content/p2152hm3v2m7t552/PublisherUNSPECIFIED
Additional Information:© 1977. Received March 25, 1976. We thank S. ANTMAN, Y. CHOQUET-BRUHAT and A. FISCHER for several useful remarks. This work was partially supported by NSF grants GP-37780X and MPS-75-05576. Communicated by S. ANTMAN
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NSFGP-37780X
NSFMPS-75-05576
Record Number:CaltechAUTHORS:20100817-114853033
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20100817-114853033
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19472
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:17 Aug 2010 20:42
Last Modified:26 Dec 2012 12:19

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