| Abstract: |
| In this paper, we study the \textit{stochastic heat equation} (SHE) on $\R^d$
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~[AOP`19], where the one-dimensional SHE on
$[0,1]$ subject to space-time white noise has been studied. This talk is based
on a jointwork with Jingyu Huang. |
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