A Remark on Uniformly Symmetrizable Systems

We prove that any first order system, in one space variable, with analytic coefficients depending only on time, is smoothly symmetrizable if and only if it is uniformly symmetrizable. Thus any one of these conditions is sufficient for the well posedness in C∞.

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2001-03, Vol.158 (1), p.18-25
Main Authors: D'Ancona, Piero, Spagnolo, Sergio
Format: Article
Language:English
Subjects:
Cauchy problem
Linear hyperbolic systems
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Summary:We prove that any first order system, in one space variable, with analytic coefficients depending only on time, is smoothly symmetrizable if and only if it is uniformly symmetrizable. Thus any one of these conditions is sufficient for the well posedness in C∞.
ISSN:0001-8708
1090-2082
DOI:10.1006/aima.2000.1957