类Cantor集上分形拉普拉斯算子定义的随机波动方程

IF 1.1 2区数学 Q1 MATHEMATICS

Publications of the Research Institute for Mathematical Sciences Pub Date : 2019-10-17 DOI:10.4171/prims/58-4-3

Tim Ehnes

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引用次数: 2

摘要

我们研究了类Cantor集上由分形拉普拉斯算子定义的Walsh意义上的随机波动方程。为此，我们对本征函数的一致范数给出了一个改进的估计，并利用预解函数密度近似了波的传播子。然后，我们建立了随机波动方程的温和解的存在性和唯一性，给出了一些Lipschitz和线性增长条件。我们证明了H在空间和时间上的较老连续性，并计算了H的较老指数。此外，我们关注的是弱间歇现象。

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Stochastic Wave Equations Defined by Fractal Laplacians on Cantor-Like Sets

We study stochastic wave equations in the sense of Walsh defined by fractal Laplacians on Cantor-like sets. For this purpose, we give an improved estimate on the uniform norm of eigenfunctions and approximate the wave propagator using the resolvent density. Afterwards, we establish existence and uniqueness of mild solutions to stochastic wave equations provided some Lipschitz and linear growth conditions. We prove H\"older continuity in space and time and compute the H\"older exponents. Moreover, we are concerned with the phenomenon of weak intermittency.

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来源期刊

Publications of the Research Institute for Mathematical Sciences 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The aim of the Publications of the Research Institute for Mathematical Sciences (PRIMS) is to publish original research papers in the mathematical sciences.