Abstract:We establish finite time extinction with probability one for weak solutions of the Cauchy-Dirichlet problem for the 1D stochastic porous medium equation with Stratonovich transport noise and compactly supported smooth initial datum. Heuristically, this is expected to hold because Brownian motion has average spread rate O(t 1 2 ) whereas the support of solutions to the deterministic PME grows only with rate O(t 1 m+1 ). The rigorous proof relies on a contraction principle up to time-dependent shift for Wong-Zak… Show more
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