| Abstract: |
| The talk is devoted to the analysis of the Cauchy-Dirichlet problem for a class of third-order hyperbolic differential operators in a domain of $\mathbb{R}^3$. The study begins to establish a priori estimates, both local and global, which play a crucial role in controlling the behavior of solutions. These estimates are established through careful analytical procedures that take into account the structure of the operators under consideration. By combining the obtained estimates with appropriate pseudo-differential techniques, an existence theorem is proved. |
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