图上的p-Laplacian方程解的性质及其数值仿真

Properties of the Solution for the p- Laplacian Equation on Graphs and Its Numerical Simulation

本文通过研究图上的p-Laplacian算子的基本性质,首先讨论了图上的p-Laplacian方程解的性质;其次,给出了一个图上的p-Laplacian方程的解析解论证了理论上的结果;最后,对另一个图上的p-Laplacian方程进行数值模拟验证理论上的结果。

Throughout the researches on the basic properties of the p- Laplacian operator,the properties of the solution for the p-Laplacian equation on graphs were considered. Finally,the analytic solution of an example for the p- Laplacian equation on a special graph is used to demonstrate the theoretical results. Furthermore,the numerical simulation for the p- Laplacian equation on a complex graph is given.