带有奇异吸收项的离散的p, ω-Laplacian方程解的淬灭现象
Quenching of the Solution of the Discrete p, ω-Laplacian Equation with Absorption Singularity Term on Graphs
DOI: 10.12677/PM.2018.84058, PDF,  被引量    科研立项经费支持
作者: 李亚峰*, 辛 巧：伊犁师范学院，数学与统计学院，新疆 伊宁
关键词: 图；p ω-Laplacian算子；淬灭；比较原理；Graph； p ω-Laplacian Operator； Quenching； Comparison Principle
摘要: 本文主要考虑了在狄利克雷边界条件下带有奇异吸收项的离散的p, ω-Laplacian方程解的淬灭现象，首先，利用巴拿赫不动点定理证明其方程局部解的存在与唯一性，其次，通过比较原理证明在一定条件下方程解在有限时间淬灭，另外，还得到其解的淬灭时间上界估计。
Abstract: This paper mainly studies the quenching of solution of the discrete p, ω-Laplacian equation with absorption singularity term and positive Dirichlet boundary conditions. First, the local existence and uniqueness of solutions are obtained by Banach fixed point theorem. And then, on some suit-able conditions, we prove that the solution quenches in finite time by comparison principle. Moreover, the upper of quenching time to solution is also obtained.
文章引用：李亚峰, 辛巧. 带有奇异吸收项的离散的p, ω-Laplacian方程解的淬灭现象[J]. 理论数学, 2018, 8(4): 436-444. https://doi.org/10.12677/PM.2018.84058

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