Numerical-mathematical methods for Hyperbolic-Parabolic Systems: Investigation of Volter-Gursat Equation and Green's Function in Three-Dimensional Spaces

This paper deals with the analysis of hyperbolic-parabolic systems with a focus on the Volter-Gursat equation and the application of Green's function in three-dimensional spaces. We explore the mathematical methods that enable the solution of these equations, including theoretical approaches and numerical techniques. Special emphasis is placed on the formulation and analysis of three-dimensional environment problems, where Green's functions are used to efficiently solve differential equations. Concrete examples and simulation results are presented that confirm the effectiveness of the proposed methods. Keywords: Hyperbolic equations, Parabolic equations, Volter-Gursat equation, Green's function, Three-dimensional environments, Mathematical analysis, Numerical methods, Differential equations.

本文针对双曲-抛物方程组开展分析研究，重点聚焦Volter-Gursat方程与格林函数(Green's function)在三维空间中的应用。本文探讨了求解此类方程的各类数学方法，涵盖理论推导路径与数值计算技术。研究特别侧重三维环境问题的建模与分析，其中借助格林函数可高效求解微分方程(Differential equations)。文中给出具体算例与仿真结果，验证了所提方法的有效性。关键词：双曲方程(Hyperbolic equations)、抛物方程(Parabolic equations)、Volter-Gursat方程、格林函数、三维环境(Three-dimensional environments)、数学分析(Mathematical analysis)、数值方法(Numerical methods)、微分方程。