Abstract

We considered the mixed parabolic-hyperbolic type equation with discontinuous coefficient in a rectangular domain.We established a criterion for the unique solvability of this problem,using this criterion constructed solution as the sum of Fourier series. Finally, the stability of the solution with respect to initial function is proved.

中文翻译：

---

矩形域中混合型方程的初边值问题

摘要

我们考虑了在矩形域中具有不连续系数的混合抛物线-双曲线型方程。我们建立了该问题唯一可解性的判据，利用该判据构造了傅里叶级数的和。最后，证明了该解相对于初始函数的稳定性。