The Cauchy\u2013Neumann and Cauchy\u2013Robin problems for a class of hyperbolic operators with double characteristics in presence of transition

Abstract

The mixed Cauchy–Neumann and Cauchy–Robin problems for a class of hyperbolic operators with double characteristics in presence of transition is investigated. Some a priori estimates in Sobolev spaces with negative indexes are proved. Subsequently, existence and uniqueness results for the mixed problems are obtained.