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  1. ; ( , Journal of Differential Equations)
    Free, publicly-accessible full text available October 1, 2022
  2. ; ; ( , Archive for Rational Mechanics and Analysis)
    Free, publicly-accessible full text available September 1, 2022
  3. ; ; ( , Journal of Differential Equations)
    Free, publicly-accessible full text available September 1, 2022
  4. ; ; ( , Journal of Inverse and Ill-posed Problems)
    Abstract We consider the 𝑑-dimensional Boussinesq system defined on a sufficiently smooth bounded domain and subject to a pair { v , u } \{v,\boldsymbol{u}\} of controls localized on { Γ ~ , ω } \{\widetilde{\Gamma},\omega\} .Here, 𝑣 is a scalar Dirichlet boundary control for the thermal equation, acting on an arbitrarily small connected portion Γ ~ \widetilde{\Gamma} of the boundary Γ = ∂ ⁡ Ω \Gamma=\partial\Omega .Instead, 𝒖 is a 𝑑-dimensional internal control for the fluid equation acting on an arbitrarily small collar 𝜔 supported by Γ ~ \widetilde{\Gamma} .The initial conditions for both fluid and heat equations aremore »taken of low regularity.We then seek to uniformly stabilize such Boussinesq system in the vicinity of an unstable equilibrium pair, in the critical setting of correspondingly low regularity spaces, by means of an explicitly constructed, finite-dimensional feedback control pair { v , u } \{v,\boldsymbol{u}\} localized on { Γ ~ , ω } \{\widetilde{\Gamma},\omega\} .In addition, they will be minimal in number and of reduced dimension; more precisely, 𝒖 will be of dimension ( d - 1 ) (d-1) , to include necessarily its 𝑑-th component, and 𝑣 will be of dimension 1.The resulting space of well-posedness and stabilization is a suitable, tight Besov space for the fluid velocity component (close to L 3 ⁢ ( Ω ) \boldsymbol{L}^{3}(\Omega) for d = 3 d=3 ) and a corresponding Besov space for the thermal component, q > d q>d .Unique continuation inverse theorems for suitably over-determined adjoint static problems play a critical role in the constructive solution.Their proof rests on Carleman-type estimates, a topic pioneered by M. V. Klibanov since the early 80s.« less
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  5. ; ; ( , Applied Mathematics & Optimization)
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  6. ; ( , Applied Mathematics & Optimization)
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  7. ; ; ( , Semigroups of Operators – Theory and Applications)
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  8. ( , Semigroups of Operators – Theory and Applications)
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  9. ; ; ( , Discrete & Continuous Dynamical Systems - B)
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  10. ; ; ( , Journal of Evolution Equations)
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