Cauchy problem for a class of nondiagonalizable hyperbolic systems

Todor Gramchev; Nicola Orrú

doi:10.3934/proc.2011.2011.533

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2011, Volume 2011: 533-542. Doi: 10.3934/proc.2011.2011.533 open access

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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

Received: June 30, 2010

Revised: February 28, 2011

Published: August 2017

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Abstract

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.

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Mathematics Subject Classification: Primary: 35L45, 35G10; Secondary: 35B30.

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