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Award ID contains: 2306221

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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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