论文标题
$ \ mathbb {r}^d $上的超线性随机热方程
Superlinear stochastic heat equation on $\mathbb{R}^d$
论文作者
论文摘要
在本文中，我们在$ \ mathbb {r}^d $上研究随机热量方程式（SHA），其含量是白色的，该噪声是白色的，在太空中是白色的。在存在局部Lipschitz漂移和扩散系数的情况下，我们建立了随机场解决方案的存在和独特性，这些系数可能具有一定的超线性生长。这是Dalang，Khoshnevisan和Zhang（2019）最近作品的非平地延伸，在这里研究了一维她在$ [0,1]上的一维她，但已经研究了时空白噪声。
In this paper, we study the stochastic heat equation (SHE) on $\mathbb{R}^d$ subject to a centered Gaussian noise that is white in time and colored in space. We establish the existence and uniqueness of the random field solution in the presence of locally Lipschitz drift and diffusion coefficients, which can have certain superlinear growth. This is a nontrivial extension of the recent work by Dalang, Khoshnevisan and Zhang (2019), where the one-dimensional SHE on $[0,1]$ subject to space-time white noise has been studied.
