Abstract

Multi-point initial boundary value problem for fourth order system of partial differential equations is considered. By new unknown function the problem is reduced to an equivalent nonlocal problem for system of hyperbolic equations of second order with dynamical condition. By the method of introduction functional parameters are constructed the algorithms for finding of solution to nonlocal problem for system of hyperbolic equations of second order with dynamical condition. Conditions of existence unique classical solution to nonlocal problem for system of hyperbolic equations of second order with dynamical condition are obtained in the terms of initial data. Criteria of unique solvability to multi-point initial boundary value problem for fourth order system of partial differential equations is established.

中文翻译：

---

偏微分方程非经典系统的多点初始问题

摘要

考虑了偏微分方程四阶系统的多点初始边值问题。通过新的未知函数，该问题被简化为带动态条件的二阶双曲方程组的等效非局部问题。利用引入的方法，构造了具有动态条件的二阶双曲方程组非参数问题求解算法。根据初始数据，获得了具有动力条件的二阶双曲方程组非局部问题存在唯一经典解的存在条件。建立了偏微分方程四阶系统多点初始边值问题的唯一可解性准则。