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2011, 2011(Special): 533-542. doi: 10.3934/proc.2011.2011.533

Cauchy problem for a class of nondiagonalizable hyperbolic systems

Todor Gramchev 1, and  Nicola Orrú 1,

1. 

Dipartimento di Matematica e Informatica, Università di Cagliari, Via Ospedale 72, 09124 Cagliari, Italy, Italy

Received  July 2010 Revised  March 2011 Published  October 2011

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.
Keywords: hyperbolic systems, nilpotent, Cauchy problem, iterative scheme.
Mathematics Subject Classification: Primary: 35L45, 35G10; Secondary: 35B30.
Citation: Todor Gramchev, Nicola Orrú. Cauchy problem for a class of nondiagonalizable hyperbolic systems. Conference Publications, 2011, 2011 (Special) : 533-542. doi: 10.3934/proc.2011.2011.533
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