Carleman estimates for a stochastic degenerate parabolic equation and applications to null controllability and an inverse random source problem

Bin Wu; Qun Chen; Zewen Wang

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arxiv 1910.14561 v2 pith:FTHV6HTC submitted 2019-10-31 math.OC

Carleman estimates for a stochastic degenerate parabolic equation and applications to null controllability and an inverse random source problem

Bin Wu , Qun Chen , Zewen Wang This is my paper

classification math.OC

keywords degenerateequationparabolicstochasticcarlemanforwardcontrollabilityestimates

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In this paper, we establish two Carleman estimates for a stochastic degenerate parabolic equation. The first one is for the backward stochastic degenerate parabolic equation with singular weight function. Combining this Carleman estimate and an approximate argument, we prove the null controllability of the forward stochastic degenerate parabolic equation with the gradient term. The second one is for the forward stochastic degenerate parabolic equation with regular weighted function, based on which we obtain the Lipschitz stability for an inverse problem of determining a random source depending only on time in the forward stochastic degenerate parabolic equation.

Carleman estimates for a stochastic degenerate parabolic equation and applications to null controllability and an inverse random source problem

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