Carleman Estimates and Controllability of Stochastic degenerate parabolic Heat Equations

Summary · qwen2.5:32b

The paper establishes global Carleman estimates to prove null controllability for both forward and backward stochastic degenerate parabolic heat equations, achieving full control with two distinct controllers for the forward equation. Notably, it introduces a new Carleman estimate for the backward equation using a non-vanishing at t=0 weighted function, crucial for proving null controllability of the forward equation via the duality method HUM.

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Excerpt

arXiv:2202.10070v2 Announce Type: replace Abstract: This paper concerns the null controllability for a class of stochastic degenerate parabolic equations. We first establish a global Carleman estimate for a linear forward stochastic degenerate equation with multiplicative noise. Using this estimate we prove the null controllability of the backward equation and obtain a partial result for the controllability of the forward equation. Also, using a new Carleman estimate for backward equation with weighted function which does not vanish at time t = 0 and the duality method HUM we get the null controllability of a forward stochastic degenerate equation under the action of two controls.