Journal
APPLIED MATHEMATICS AND OPTIMIZATION
Volume 47, Issue 2, Pages 97-120Publisher
SPRINGER-VERLAG
DOI: 10.1007/s00245-002-0757-z
Keywords
stochastic PDEs; controllability; backward stochastic equations; Carleman estimates
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This work is concerned with Carleman inequalities and controllability properties for the following stochastic linear heat equation (with Dirichlet boundary conditions in the bounded domain D subset of R-d and multiplicative noise): {d(t)y(u) - Deltay(u) + ay(u)dt = f dt + 1(D0)u dt + bydbeta(t) in ]0, T] x D, y(u) = 0 on ]0,T] x partial derivativeD, y(u)(0) = y(0) in D, and for corresponding backward dual equation: {d(t)p(nu) + Deltap(nu)dt - ap(nu)dt + bk(nu)dt = 1(D0)nudt + k(nu)dbeta(t) in [0,T[ x D, p(nu) = 0 on [0,T[ x partial derivativeD, p(nu)(T) = eta in D. We prove the null controllability of the backward euation and obtain partial results for the controllability of the forward equation.
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