Showing papers by "Yi-Hsuan Lin published in 2018"
16 Nov 2018
TL;DR: In this article, the authors study global uniqueness in an inverse problem for the fractional semilinear Schrödinger equation (−∆)su + q(x, u) = 0 with s ∈ (0, 1) for any space dimension greater than or equal to 2.
Abstract: We study global uniqueness in an inverse problem for the fractional semilinear Schrödinger equation (−∆)su + q(x, u) = 0 with s ∈ (0, 1). We show that an unknown function q(x, u) can be uniquely determined by the Cauchy data set. In particular, this result holds for any space dimension greater than or equal to 2. Moreover, we demonstrate the comparison principle and provide a L∞ estimate for this nonlocal equation under appropriate regularity assumptions.
63 citations
TL;DR: In this paper, the authors consider field localizing and concentration of electromagnetic waves governed by the time-harmonic anisotropic Maxwell system in a bounded domain and show that there always exist certain bou...
Abstract: We consider field localizing and concentration of electromagnetic waves governed by the time-harmonic anisotropic Maxwell system in a bounded domain. It is shown that there always exist certain bou...
23 citations
Posted Content•
TL;DR: In this article, the Calder\'on problem with drift was studied and it was shown that the unknown drift and potential in a bounded domain can be determined simultaneously and uniquely by an infinite number of exterior measurements.
Abstract: We investigate the Calder\'on problem for the fractional Schr\"odinger equation with drift, proving that the unknown drift and potential in a bounded domain can be determined simultaneously and uniquely by an infinite number of exterior measurements. In particular, in contrast to its local analogue, this nonlocal problem does \emph{not} enjoy a gauge invariance. The uniqueness result is complemented by an associated logarithmic stability estimate under suitable apriori assumptions. Also uniqueness under finitely many \emph{generic} measurements is discussed. Here the genericity is obtained through \emph{singularity theory} which might also be interesting in the context of hybrid inverse problems. Combined with the results from \cite{GRSU18}, this yields a finite measurements constructive reconstruction algorithm for the fractional Calder\'on problem with drift. The inverse problem is formulated as a partial data type nonlocal problem and it is considered in any dimension $n\geq 1$.
21 citations
TL;DR: In this article, the inverse source problem of a fixed frequency for the Navier's equation was studied and it was shown that if the support of such a force has a convex or non-convex corner or edge on their boundary, the force must be vanishing there.
Abstract: In this work, we study the inverse source problem of a fixed frequency for the Navier's equation. We investigate that nonradiating external forces. If the support of such a force has a convex or non-convex corner or edge on their boundary, the force must be vanishing there. The vanishing property at corners and edges holds also for sufficiently smooth transmission eigenfunctions in elasticity. The idea originates from the enclosure method: The energy identity and new type exponential solutions for the Navier's equation.
9 citations
TL;DR: It is shown that there always exist certain boundary inputs which can generate electromagnetic fields with the energy localized/concentrated in a given sub domain while nearly vanishing in another given subdomain.
Abstract: We consider field localizing and concentration of electromagnetic waves governed by the time-harmonic anisotropic Maxwell system in a bounded domain. It is shown that there always exist certain boundary inputs which can generate electromagnetic fields with energy localized/concentrated in a given subdomain while nearly vanishing in another given subdomain. The theoretical results may have potential applications in telecommunication, inductive charging and medical therapy. We also derive a related Runge approximation result for the time-harmonic anisotropic Maxwell system with partial boundary data.
9 citations
Posted Content•
01 Oct 2018
TL;DR: In this article, the Calderon problem for the fractional Schrodinger equation with drift is studied and it is shown that the unknown drift and potential in a bounded domain can be determined simultaneously and uniquely by an infinite number of exterior measurements.
Abstract: We investigate the Calderon problem for the fractional Schrodinger equation with drift, proving that the unknown drift and potential in a bounded domain can be determined simultaneously and uniquely by an infinite number of exterior measurements. In particular, in contrast to its local analogue, this nonlocal problem does not enjoy a gauge invariance. The uniqueness result is complemented by an associated logarithmic stability estimate under suitable apriori assumptions. Also uniqueness under finitely many generic measurements is discussed. Here the genericity is obtained through singularity theory which might also be interesting in the context of hybrid inverse problems. Combined with the results from Ghosh et al. (Uniqueness and reconstruction for the fractional Calderon problem with a single easurement, 2018. arXiv:1801.04449), this yields a finite measurements constructive reconstruction algorithm for the fractional Calderon problem with drift. The inverse problem is formulated as a partial data type nonlocal problem and it is considered in any dimension $$n\ge 1$$.
5 citations
Posted Content•
TL;DR: In this paper, the scattering of elastic waves by highly oscillating anisotropic periodic media with bounded support was considered and a constant coefficient second-order partial differential elliptic equation was derived to describe the wave propagation of the effective or overall wave field.
Abstract: We consider the scattering of elastic waves by highly oscillating anisotropic periodic media with bounded support Applying the two-scale homogenization, we first obtain a constant coefficient second-order partial differential elliptic equation that describes the wave propagation of the effective or overall wave field We study the rate of convergence by introducing complimentary boundary correctors To account for dispersion induced by the periodic structure, we further pursue a higher-order homogenization We then investigate the rate of convergence and formally obtain a fourth-order differential equation that demonstrates the anisotropic dispersion