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The First Boundary Problem with an Integral Condition for a Mixed-Type Equation with a Characteristic Degeneration
Russian Mathematics Pub Date : 2020-12-25 , DOI: 10.3103/s1066369x20110043
Yu. K. Sabitova

In this paper, we study the first boundary problem for a mixed-type elliptic-hyperbolic equation of the second kind in a rectangular domain. We construct the problem solution as the sum of a biorthogonal series and prove the uniqueness criterion for it. When proving the existence of the problem solution, we encounter the problem of small denominators. In this connection, we establish estimates for the separation of denominators from zero with the corresponding asymptotics; this allows us to justify the existence of a solution in the class of regular solutions.



中文翻译:

具有特征退化的混合型方程的积分条件的第一个边界问题

在本文中,我们研究了矩形域中第二种混合型椭圆双曲型方程的第一边界问题。我们将问题解决方案构造为双正交序列的总和,并证明其唯一性准则。在证明问题解决方案的存在时,我们遇到了小分母的问题。在这一点上,我们建立了分母与零的分离以及相应的渐近性的估计。这使我们能够在常规解决方案类别中证明解决方案的存在性。

更新日期:2020-12-25
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