Existence results for the mixed Cauchy–Dirichlet problem for a class of hyperbolic operators

The paper concerns the study of the Cauchy–Dirichlet problem for a class of hyperbolic second-order operators with double characteristics in presence of transition in a domain of $${\mathbb {R}}^3$$ R 3 . Firstly, we establish some a priori local and global estimates. Then, we obtain some existence results.

On the Cauchy problem for a class of hyperbolic operators with triple characteristics

The Cauchy problem for a class of hyperbolic operators with triple characteristics is analyzed. Some a priori estimates in Sobolev spaces with negative indexes are proved. Subsequently, an existence result for the Cauchy problem is obtained.

The Cauchy–Neumann and Cauchy–Robin problems for a class of hyperbolic operators with double characteristics in presence of transition

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.