Study on the Definite Solution Problems for Systems of Partial Differential Equations under Elastic External Boundary Condition of Polynomial Function Type and Application in Composite Reservoir

This paper establishes the definite solution problems for systems of partial differential equations (PDEs) under polynomial function type of external boundary conditions. Then the related theorems and solving method—Laplace transformation—improved similarity construction method—Gaver–Stehfest numerical inversion (LT-ISCM-GSNI) method of the solution to the definite solution problem are provided. Based on the solution method, the steps for solving the definite solution problem are summarized. Finally, using LT-ISCM-GSNI method, this paper gives application in solving composite reservoir seepage model under elastic external boundary condition of polynomial function type. The introduction of functional elastic outer boundary conditions not only expands the research scope of definite solution problems for partial differential equation (system), but also improves the matching degree between the theoretical model and the actual problems.