The Cauchy–Dirichlet problem for a class of hyperbolic operators with double characteristics in the presence of transition

Abstract The paper deals with the study of the Cauchy–Dirichlet problem for the class of hyperbolic second order operators with double characteristics in the presence of transition P = D x 0 2 − D x 1 2 − ( x 0 + λ − α ( x 1 ) ) 2 D x 2 2 . Energy estimates and existence and uniqueness results are established.