Electron. J. Differential Equations, Vol. 2019 (2019), No. 130, pp. 1-54.

Necessary and sufficient conditions for hyperbolicity and weak hyperbolicity of systems with constant multiplicity, part I

Giovanni Taglialatela, Jean Vaillant

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
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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