Zobrazeno 1 - 10
of 153
pro vyhledávání: '"Lai, Ru"'
In this paper, we study the partial data inverse problem for nonlinear magnetic Schr\"odinger equations. We show that the knowledge of the Dirichlet-to-Neumann map, measured on an arbitrary part of the boundary, determines the time-dependent linear c
Externí odkaz:
http://arxiv.org/abs/2411.06369
Autor:
Lai, Ru-Yu, Zhou, Hanming
In this work, we investigate inverse problems of recovering the time-dependent coefficient in the nonlinear transport equation in both cases: two-dimensional Riemannian manifolds and Euclidean space $\mathbb{R}^n$, $n\geq 2$. Specifically, it is show
Externí odkaz:
http://arxiv.org/abs/2410.00369
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 t
Externí odkaz:
http://arxiv.org/abs/2401.04834
Autor:
Lai, Ru-Yu, Yan, Lili
We consider an inverse problem for the nonlinear Boltzmann equation with a time-dependent kernel in dimensions $n\ge 2$. We establish a logarithm-type stability result for the collision kernel from measurements under certain additional conditions. A
Externí odkaz:
http://arxiv.org/abs/2309.03368
In this paper we prove the uniqueness and stability in determining a time-dependent nonlinear coefficient $\beta(t, x)$ in the Schr\"odinger equation $(i\partial_t + \Delta + q(t, x))u + \beta u^2 = 0$, from the boundary Dirichlet-to-Neumann (DN) map
Externí odkaz:
http://arxiv.org/abs/2306.15935
We consider the inverse problem for time-dependent semilinear transport equations. We show that time-independent coefficients of both the linear (absorption or scattering coefficients) and nonlinear terms can be uniquely determined, in a stable way,
Externí odkaz:
http://arxiv.org/abs/2207.10194
In this paper, we analyze the nonlinear single pixel X-ray transform $K$ and study the reconstruction of $f$ from the measurement $Kf$. Different from the well-known X-ray transform, the transform $K$ is a nonlinear operator and uses a single detecto
Externí odkaz:
http://arxiv.org/abs/2112.13978
Motivated by applications in imaging nonlinear optical absorption by photoacoustic tomography (PAT), we study in this work inverse coefficient problems for a semilinear radiative transport equation and its diffusion approximation with internal data t
Externí odkaz:
http://arxiv.org/abs/2107.08118
Autor:
Lai, Ru-Yu, Zhou, Hanming
This paper is concerned with the inverse source problem for the transport equation with external force. We show that both direct and inverse problems are uniquely solvable for generic absorption and scattering coefficients. In particular, for inverse
Externí odkaz:
http://arxiv.org/abs/2104.11851
Autor:
Lai, Ru-Yu, Zhou, Ting
In this paper, we study forward problem and inverse problem for the fractional magnetic Schrodinger equation with nonlinear electric potential. We first investigate the maximum principle for the linearized equation and apply it to show that the probl
Externí odkaz:
http://arxiv.org/abs/2103.08180