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Global regularity and formation of singularities of solutions to first order quasilinear hyperbolic systems

Published online by Cambridge University Press:  14 November 2011

Lee Da-tsin(Li Ta-tsien)
Lee Da-tsin(Li Ta-tsien)
Affiliation:
Department of Mathematics, Fudan University, Shanghai, China and Collège de France, Paris, France
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Synopsis

For the Cauchy problem for strictly hyperbolic systems with general eigenvalues, we obtain existence of global smooth solutions under certain conditions on the composition of the eigenvalues and the initial data; on the other hand, we give a sufficient condition which guarantees that singularities of the solution must occur in a finite time and describe certain applications. The present paper includes the corresponding results in earlier papers by several authors as special cases.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 87 , Issue 3-4 , 1981 , pp. 255 - 261
Copyright
Copyright © Royal Society of Edinburgh 1981

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