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Award ID contains: 2006731

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  1. ; ; (, Inverse Problems)
    Abstract We study the inverse problem of recovering the doping profile in the stationary Vlasov–Poisson equation, given the knowledge of the incoming and outgoing measurements at the boundary of the domain. This problem arises from identifying impurities in the semiconductor manufacturing. Our result states that, under suitable assumptions, the doping profile can be uniquely determined through an asymptotic formula of the electric field that it generates. 
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  2. ; (, SIAM Journal on Applied Mathematics)
    We consider an inverse problem for the nonlinear Boltzmann equation with a time-dependent kernel in dimensions n \geq 2. We establish a logarithm-type stability result for the collision kernel from measurements under certain additional conditions. A uniqueness result is derived as an immediate consequence of the stability result. Our approach relies on second-order linearization and multivariate finite differences, as well as the stability of the light-ray transform. 
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  3. ; ; (, SIAM Journal on Mathematical Analysis)
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  4. ; ; (, Archive for Rational Mechanics and Analysis)
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  5. ; (, Journal of Differential Equations)
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  6. ; (, Mathematical Research Letters)
    We prove that the knowledge of the Dirichlet-to-Neumann map, measured on a part of the boundary of a bounded domain in Rn, n\geq 2, can uniquely determine, in a nonlinear magnetic Schrödinger equation, the vector-valued magnetic potential and the scalar electric potential, both being nonlinear in the solution. 
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  7. ; ; ; (, SIAM Journal on Imaging Sciences)
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  8. ; ; (, SIAM Journal on Applied Mathematics)
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  9. ; (, Inverse Problems & Imaging)
    We study the inverse problem for the fractional Laplace equation with multiple nonlinear lower order terms. We show that the direct problem is well-posed and the inverse problem is uniquely solvable. More specifically, the unknown nonlinearities can be uniquely determined from exterior measurements under suitable settings. 
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  10. ; (, Journal of Differential Equations)
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