Giovanni Taglialatela, Jean Vaillant
Abstract:
We consider a linear system of partial differential equations,
whose principal symbol is hyperbolic with characteristics
of constant multiplicities.
We define necessary and sufficient invariant condition
in order the Cauchy problem to be well-posed in C^infinity.
These conditions generalize the Levi conditions for scalar operators.
The proof is based on the construction of a new non commutative determinant
adapted to this case (and to the holomorphic case).
Submitted May 15, 2019. Published December 9, 2019.
Math Subject Classifications: 35L45
Key Words: Cauchy problem; systems with constant multiplicity; Levi conditions.
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Giovanni Taglialatela University of Bari Dipartimento di Economia e Finanza Largo Abbazia S. Scolastica 70124 Bari, Italy email: giovanni.taglialatela@uniba.it |
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Jean Vaillant Sorbonne Universite Institut de Mathematiques de Jussieu Paris Gauche BC 247, 4 Place Jussieu 75252 Paris Cedex 05, France email: jean.vaillant@upmc.fr |
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