Null controllability for one-dimensional stochastic heat equations with mixed Dirichlet-dynamic boundary conditions

被引:3
作者
Baroun, Mahmoud [1 ]
Boulite, Said [2 ]
Elgrou, Abdellatif [1 ]
Maniar, Lahcen [1 ]
机构
[1] Cadi Ayyad Univ, Fac Sci Semlalia, LMDP, UMMISCO IRD UPMC, BP 2390, Marrakech, Morocco
[2] Cadi Ayyad Univ, Natl Sch Appl Sci, LMDP, UMMISCO IRD UPMC, BP 575, Marrakech, Morocco
关键词
Null controllability; stochastic heat equations; Carleman estimates; observability inequality; dynamic boundary conditions; PARABOLIC EQUATIONS; CARLEMAN INEQUALITIES; UNIQUE CONTINUATION;
D O I
10.1051/cocv/2024082
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
In this paper, we study the null controllability of one-dimensional forward and backward linear stochastic heat equations with mixed Dirichlet-dynamic boundary conditions. Our equations incorporate noise not only within the domain but also at the boundary, represented by a two-dimensional Brownian motion. The primary tool will be global Carleman estimates, which yield the appropriate observability inequalities for the related adjoint systems. Hence, by classical duality arguments, we establish the corresponding null controllability results. Specifically, we first establish a Carleman estimate for a general adjoint backward stochastic heat equation using a weighted identity method. This approach combines two weighted identities: one for a stochastic parabolic operator and the other for a stochastic transport operator. Subsequently, we derive a Carleman estimate for a general adjoint forward stochastic heat equation by employing a duality method.
引用
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页数:31
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