Cantor类集上分形Laplacian定义的随机Heat Equations
Stochastic Heat Equations defined by Fractal Laplacians on Cantor-like Sets
摘要：
本文研究了Cantor类集上由分形Laplacian定义的Walsh意义下的随机热方程。为此，我们首先研究相应的热核。然后，我们证明了随机热方程温和解的存在性和唯一性提供了一些Lipschitz和线性增长条件。我们建立了空间和时间上的Hölder连续性，并计算了Hölder指数。此外，我们解决的问题，弱不连续性。
英文摘要：
We study stochastic heat equations in the sense of Walsh defined by fractal Laplacians on Cantor-like sets. For this purpose, we first investigate the corresponding heat kernels. Then, we prove existence and uniqueness of mild solutions to stochastic heat equations provided some Lipschitz and linear growth conditions. We establish Hölder continuity in space and time and compute the Hölder exponents. Moreover, we address the question of weak intermittency.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
