Electronic Journal of Differential Equations, 
Vol. 2019 (2019), No. 130, pp. 1-54.

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

Authors: Giovanni Taglialatela (Univ. of Bari, Bari, Italy)
               Jean Vaillant (Sorbonne Univ., Paris, France)

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.