Null controllability for backward stochastic parabolic convection-diffusion equations with dynamic boundary conditions

Baroun, Mahmoud; Boulite, Said; Elgrou, Abdellatif; Maniar, Lahcen

doi:10.3934/mcrf.2024031

MCRF

2024

DOI: 10.3934/mcrf.2024031

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Null controllability for backward stochastic parabolic convection-diffusion equations with dynamic boundary conditions

Mahmoud Baroun,

Said Boulite,

Abdellatif Elgrou

et al.

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2024

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

Baroun,

Boulite,

Elgrou

et al. 2024

ESAIM: COCV

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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.

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

Baroun,

Boulite,

Elgrou

et al. 2024

ESAIM: COCV

View full text Add to dashboard Cite

show abstract

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Null controllability for backward stochastic parabolic convection-diffusion equations with dynamic boundary conditions

Cited by 1 publication

References 35 publications

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

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

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