Necessary and sufficient conditions for hyperbolicity and weak hyperbolicity of systems with constant multiplicity, part I
Date
2019-12-09
Authors
Taglialatela, Giovanni
Vaillant, Jean
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
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∞. 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).
Description
Keywords
Cauchy problem, Systems with constant multiplicity, Levi conditions
Citation
Taglialatela, G., & Vaillant, J. (2019). Necessary and sufficient conditions for hyperbolicity and weak hyperbolicity of systems with constant multiplicity, part I. <i>Electronic Journal of Differential Equations, 2019</i>(130), pp. 1-54.