混合局部-非局部抛物型系统淬灭问题的移动平面法
A method of moving planes for a mixed local-nonlocal parabolic system with quenching
浏览论文内容
中文总结 AI 辅助
本文为混合局部-非局部扩散系统发展抛物型移动平面法，证明奇异吸收项下淬灭发生的参数范围、全局解存在性及淬灭区域的紧性。
中文摘要 AI 辅助
本文针对具有混合局部与非局部扩散算子（即 $\mathcal{L} = -(-\Delta)^s + \Delta$，其中 $(-\Delta)^s$ 为积分分数阶拉普拉斯算子）的系统，发展了移动平面法的抛物型版本。我们利用该结果研究此类系统中带有奇异吸收项 $(1-u)^{-p}$ 的淬灭现象。我们证明存在一个乘法参数范围，使得每个解都会发生淬灭；并且对于任意初始数据 $u_0$，存在足够小的乘法参数使得解全局存在。我们还证明了淬灭现象不会发生在任意靠近边界的位置，而是包含在域的一个紧子集中。
英文摘要
In this paper we develop a parabolic version of the method of moving planes on systems with a mixed local and nonlocal diffusion operator, that being $\mathcal{L} = -(-Δ)^s + Δ$, where $(-Δ)^s$ is the integral fractional laplacian. We then use this result to study the quenching phenomena occurring in said systems with a singular absorption term of the type $(1-u)^{-p}$. We prove that there exists a range of multiplicative parameters for which every solution presents quenching, and that for any initial datum $u_0$, there exists a small enough multiplicative parameter such as the solution is globally defined. We also prove that the quenching phenomena cannot happen arbitrarily close to the boundary, but they are contained in a compact subset of the domain.
发表机构
- Universidad Complutense de Madrid（马德里康普顿斯大学）
- PEDECIBA Matemática（PEDECIBA数学研究所）
机构由 AI 辅助整理，请以论文原文为准。
