| Abstract: |
| In this talk, we discuss the instantaneous shrinking of the support of solutions to one-dimensional parabolic stochastic PDEs driven by space-time white noise. It is well known that if the initial data has compact support, then the solution also has compact support for all later times. In deterministic cases, a much stronger result holds: the solution has compact support immediately after the initial time if the initial data merely vanishes uniformly at infinity. We show that a class of parabolic SPDEs also exhibits instantaneous shrinking. In particular, if the uniqueness in law holds, then all nonnegative solutions exhibit instantaneous shrinking. |
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