函数型弹性外边界条件下偏微分方程定解问题的解的相似构造
Similar Construction of Solutions to Definite Solution Problem for Partial Differential Equation with Functional Elastic External Boundary Condition
摘要: 本文主要研究了指数函数型弹性外边界条件下偏微分方程的定解问题。首先，介绍了弹性外边界条件下偏微分方程的定解问题。其次，给出了定解问题解的相关定理以及相似结构解的构造步骤，为后续求解奠定了理论基础。最后，通过运用Laplace变换法和Gaver-Stehfest数值反演法，成功解决了相关微分方程的定解问题，并得出了结论。引入函数型弹性外边界条件的研究不仅拓宽了偏微分方程定解的研究范围，同时也使得弹性外边界条件更贴合实际问题，具有更高的实用性和应用价值。本研究在理论和方法上都取得了一定的突破，为类似问题的研究提供了新的思路和方法，具有一定的学术价值和实用意义。
Abstract: In this paper, we mainly study the definite solution of partial differential equations under exponential function type elastic outer boundary conditions. Firstly, the definite solution of partial differential equations under elastic external boundary conditions is introduced, and its application in practical problems is discussed. Then, the related theorems of the solution of the definite solution problem are given, and the construction steps of the similar structure solution are introduced, which lays a theoretical foundation for the subsequent solution. Finally, by using Laplace transform method and Gaver-Stehfest numerical inversion method, the definite solution problem of related differential equations is successfully solved, and the conclusion is drawn. The research on the introduction of functional elastic external boundary conditions not only broadens the research scope of the definite solution of partial differential equations, but also makes the elastic external boundary conditions more suitable for practical problems, which has higher practicability and application value. This study has made some breakthroughs in theory and method, and provides new ideas and methods for the study of similar problems, which has certain academic value and practical significance.
文章引用：曾峥, 董晓旭, 彭钰, 梁滢, 王玉. 函数型弹性外边界条件下偏微分方程定解问题的解的相似构造[J]. 理论数学, 2024, 14(4): 73-79. https://doi.org/10.12677/pm.2024.144112

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