5 papers
The higher-order fractional Schrödinger equation with nonlinear local perturbations: Uniqueness
Giovanni Covi, Ru-Yu Lai, Lili Yan
We study the higher-order fractional Schrödinger equation with local nonlinear perturbations and investigate both the forward and inverse problems. We establish both the Sobolev $H…
Entanglement principle and fractional Calderón problem for nonlocal parabolic operators
Ru-Yu Lai, Yi-Hsuan Lin, Lili Yan
We examine inverse problems for the variable-coefficient nonlocal parabolic operator , where . This article makes two primary contributions. First,…
Partial data inverse problems for the nonlinear magnetic Schrödinger equation
Ru-Yu Lai, Gunther Uhlmann, Lili Yan
In this paper, we study the partial data inverse problem for nonlinear magnetic Schrödinger equations. We show that the knowledge of the Dirichlet-to-Neumann map, measured on an ar…
Reconstruction of the Doping Profile in Vlasov-Poisson
Ru-Yu Lai, Qin Li, Weiran Sun
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 bounda…
Stable determination of time-dependent collision kernel in the nonlinear Boltzmann equation
Ru-Yu Lai, Lili Yan
We consider an inverse problem for the nonlinear Boltzmann equation with a time-dependent kernel in dimensions . We establish a logarithm-type stability result for the coll…