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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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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description 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∞.
doi_str_mv 10.1006/aima.2000.1957
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subjects Cauchy problem
Linear hyperbolic systems
title A Remark on Uniformly Symmetrizable Systems
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