Geodesic
Unique continuation for stochastic heat equations
Lü, Qi1 ; Yin, Zhongqi2
1 School of Mathematics, Sichuan University, Chengdu 610064, P.R. China.
2 School of Mathematics, Sichuan Normal University, Chengdu 610068, P.R. China.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 2, pp. 378-398

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We establish a unique continuation property for stochastic heat equations evolving in a domain G⊂R n (n∈N). Our result shows that the value of the solution can be determined uniquely by means of its value on an arbitrary open subdomain of G at any given positive time constant. Further, when G is convex and bounded, we also give a quantitative version of the unique continuation property. As applications, we get an observability estimate for stochastic heat equations, an approximate result and a null controllability result for a backward stochastic heat equation.

Reçu le :
DOI : 10.1051/cocv/2014027
Classification : 60H15, 93B05
Keywords: Stochastic heat equations, unique continuation property, backward stochastic heat equations, approximate controllability, null controllability

Lü, Qi 1 ; Yin, Zhongqi 2

1 School of Mathematics, Sichuan University, Chengdu 610064, P.R. China.
2 School of Mathematics, Sichuan Normal University, Chengdu 610068, P.R. China. 
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     title = {Unique continuation for stochastic heat equations},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {378--398},
     publisher = {EDP-Sciences},
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Lü, Qi; Yin, Zhongqi. Unique continuation for stochastic heat equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 2, pp. 378-398. doi: 10.1051/cocv/2014027

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