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
Abstract
Abstract 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.
Topics & Concepts
Degenerate energy levelsMathematicsControllabilityLipschitz continuityParabolic partial differential equationMathematical analysisInverseUniquenessNull (SQL)Stability (learning theory)Inverse problemStochastic processStochastic differential equationApplied mathematicsHeat equationStable processBounded functionStability and Controllability of Differential EquationsNumerical methods in inverse problemsStochastic processes and financial applications