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Cauchy problem for a class of nondiagonalizable hyperbolic systems

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  • We investigate the well-posedness of Cauchy problem for weakly hyperbolic systems in one space dimension with time dependent coecients in Sobolev spaces and in the $C^\infty$ category allowing nondiagonalizable principal parts and complex entries in the nilpotent part. We prove well-posedness results by means of an iterative approach under conditions linking the characteristic roots, the entries of the nilpotent part and of the zero order part.
    Mathematics Subject Classification: Primary: 35L45, 35G10; Secondary: 35B30.


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