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.

中文翻译：

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一类双曲算子在过渡条件下具有双重特征的柯西-纽曼和柯西-罗宾问题

研究了一类在过渡条件下具有双重特征的双曲算子的混合柯西-纽曼和柯西-罗宾问题。证明了Sobolev空间中具有负索引的一些先验估计。随后，获得了混合问题的存在性和唯一性结果。