Carleman Estimates and Controllability of Linear Stochastic Heat Equations

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Strong solution of backward stochastic partial differential equations in C2 domains (2010, methodology): “. Assume that for λ= λ0 ∈ [0,1], BSPDE (5.9) has a unique strong solution (p,q) ∈ H2,1(D), for any φ∈ L2(Ω,F T ,H 1 0(D)) and any F ∈ H0(D) satisfying Assumption 5.1 and condition (5.5). For other λ∈ [0,1], we can rewrite (4.27) as dp= − aijD ijp+σ ikD iq+λ0F(t,x,p,q)+(λ−λ0)F(t,x,p,q) dt+qkdWk t . T”
Some results on the controllability of forward stochastic heat equations with control on the drift (2011, background): “As remarked in [1], it is very hard to establish the observability estimate for this system with only one observer.”
A unified controllability/observability theory for some stochastic and deterministic partial differential equations (2010, background): “1, one can show the following observability result in [41] (See [3] and the references therein for some earlier results).”
On a Time-Optimal Control Problem Associated with the Heat Exchange Process (2008, background): “More recent results concerned with this problem were established in [1, 3–5, 8–11].”