关键词: 偏微分方程组, 初边值问题, 线性算子半群, 算子级数法, 广义解

Abstract:

In consideration of the practical transient flow of complex branch-like pipeline network on loop, it is the first time that we have presented in this paper the mathematical model, which is a system of partial differential equations with initial conditions and boundary conditions, an initial-boundary value problem. We have proved that the solution of the initial-boundary value problem is existent and unique by the theory of semigroups of linear operators, and we have obtained the solution in wider sense with the operator series method.

Key words: System of Partial Differential Equations, Initial-boundary Value Problem, Semigroup of Linear Operators, Operator Series Method, Solution in Wider Sense