Abstract

In the work Tricomi problem was investigated for a parabolic-hyperbolic type equation in a mixed domain. If the parabolic degeneration line is a characteristic of a hyperbolic equation, then Tricomi problem for considered equation will not be uniquely solvable. Therefore, another formulation of Tricomi problem was proposed which the gluing condition is given as in [1, 2]. To study Tricomi problem in the hyperbolic part of the domain, \(R_{00}^{\lambda}\) class of the regular solutions of the view changed Cauchy problem for the equation of the hyperbolic part are introduced. An explicit form of the solution is found for the Cauchy problem from this class. The solution of the Tricomi problem in the hyperbolic part of the domain is found as a regular solution from the class \(R_{00}^{\lambda}\) of the view changed Cauchy problem, and in the parabolic part of the domain as the solution of the first boundary value problem. For proving the existence of the solution of the problem, the theory of second kind Volterra integral equations is used.

中文翻译：

---

第二类抛物线双曲型方程的Tricomi问题

摘要

在工作中，研究了混合区域中抛物线-双曲线型方程的Tricomi问题。如果抛物线退化线是双曲方程的特征，则考虑方程的Tricomi问题将不能唯一求解。因此，提出了Tricomi问题的另一种表示方法，其胶粘条件如[1、2]所示。为了研究域双曲部分中的Tricomi问题，引入了双曲部分方程的视变Cauchy问题正则解的（R_ {00} ^ {\ lambda} \）类。从此类中可以找到针对柯西问题的显式解决方案。从类\（R_ {00} ^ {\ lambda} \）中，找到该域双曲部分中Tricomi问题的解作为常规解。的观点改变了柯西问题，并在域的抛物线部分作为第一边值问题的解决方案。为了证明问题解的存在，使用了第二类Volterra积分方程的理论。