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Cauchy problem for a class of nondiagonalizable hyperbolic systems

Pages: 533 - 542, Issue Special, September 2011

 Abstract        Full Text (350.0K)              

Todor Gramchev - Dipartimento di Matematica e Informatica, UniversitĂ  di Cagliari, Via Ospedale 72, 09124 Cagliari, Italy (email)
Nicola OrrĂș - Dipartimento di Matematica e Informatica, UniversitĂ  di Cagliari, Via Ospedale 72, 09124 Cagliari, Italy (email)

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.

Keywords:  Cauchy problem, hyperbolic systems, iterative scheme, nilpotent
Mathematics Subject Classification:  Primary: 35L45, 35G10; Secondary: 35B30

Received: July 2010;      Revised: March 2011;      Published: October 2011.