| Abstract: |
| In this paper, we investigate stochastic heat equation with sublinear
diffusion coefficients. By assuming certain concavity of the diffusion
coefficient, we establish non-trivial moment upper bounds for the solution.
These moment bounds shed light on the \textit{smoothing intermittency effect}
under \textit{weak diffusion} (i.e., sublinear growth) previously observed by
Zeldovich {\it et al}. The method we employ is highly robust and can be
extended to a wide range of stochastic partial differential equations,
including the one-dimensional stochastic wave equation. This is a jointwork
with Panqiu Xia (Auburn University). |
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