Abstract

In this paper we study a new problem for a parabolic-hyperbolic equation with fractional order Caputo operator in rectangular domain. There are many works devoted to study problems for the second order mixed parabolic-hyperbolic and elliptic-hyperbolic type equations in rectangular domains with two gluing conditions with respect to second argument and with boundary value conditions on all borders of the domain. In studying the unique solvability of this problem, it becomes necessary to specify an additional condition on the hyperbolic boundary of the domain. For this reason, the considering problem became unresolved in an arbitrary rectangular domain. In this paper, we were able to remove this restriction by setting three gluing conditions for the second argument.

中文翻译：

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矩形域中分数阶Caputo算子的抛物线-双曲型方程的边值问题

摘要

在本文中，我们研究了矩形域中分数阶Caputo算子的抛物-双曲方程的新问题。有很多工作致力于研究矩形域中的二阶混合抛物线-双曲线型和椭圆形-双曲线型方程的问题，这些方程相对于第二个自变量具有两种胶合条件，并且在域的所有边界上都具有边值条件。在研究此问题的独特可解性时，有必要在域的双曲边界上指定一个附加条件。因此，考虑的问题在任意的矩形域中都没有解决。在本文中，我们可以通过为第二个参数设置三个粘合条件来消除此限制。