Cauchy problem in generalized Gevrey classes
Volume 60 / 2003
Banach Center Publications 60 (2003), 269-278
MSC: Primary 35L40
DOI: 10.4064/bc60-0-21
Abstract
In this work we present a class of partial differential operators with constant coefficients, called multi-quasi-hyperbolic and defined in terms of a complete polyhedron. For them we obtain the well-posedness of the Cauchy problem in generalized Gevrey classes determined by means of the same polyhedron. We present some necessary and sufficient conditions on the operator in order to be multi-quasi-hyperbolic and give some examples.
