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.