arXiv subjects

Lung-Hui Chen

Publications and source records attributed to Lung-Hui Chen.

23 records · Page 2Linked to original sources

arXiv2012

A Global Uniqueness on Spherically Stratified Dielectric Medium in Time-Harmonic Maxwell Equation with Interior Transmission Eigenvalues

A set of regularly distributed transmission eigenvalues generates a density function. We use such a density function inversely determines the form of the indicator function. Using the entire function theory, we reduce an uniqueness problem with interior transmission eigenvalues induced by time-harmonic Maxwell equation to an uniqueness problem in entire function theory. In such an inverse problem, the definite integral of the square root of refraction index is the main parameter.

math.SP↗

arXiv2012

An Uniqueness Result on Spherically Stratified Media with Interior Transmission Eigenvalues

Given a set of transmission eigenvalues, we describe the connection of such a set to the indicator functions in entire function theory. The indicator functions control the asymptotic growth rate of the solution of the Sturm-Liouville problem which has an uniqueness in the inverse spectral theory. Henceforth, the set of transmission eigenvalues has an inverse spectral property.

math.AP↗

arXiv2011

Counting the Resonances in High and Even Dimensional Obstacle Scattering

In this paper, we give a polynomial lower bound for the resonances of $-Δ$ perturbed by an obstacle in even-dimensional Euclidean spaces, $n\geq4$. The proof is based on a Poisson Summation Formula which comes from the Hadamard factorization theorem in the open upper complex plane. We take advantage of the singularity of regularized wave trace to give the pole/resonance counting function over the principal branch of logarithmic plane a lower bound.

math.FA↗

arXiv2011

A Super-Exponential Decaying Property of Odd-Dimensional Wave Scattered by an Obstacle

We examine an inverse backscattering property of wave motion imposed by an obstacle. We show that if the wave propagator decays super-exponentially along the back-scattered geodesics, then the involved scatterer must be trivial. In particular, if the fundamental solution decays super-exponentially some time after t=0, it vanishes for all time. We use finite speed of propagation in this article.

math.FA↗

arXiv2010

Uniqueness on the Class of Odd-Dimensional Starlike Obstacles with Cross Section Data

We determine the uniqueness on starlike obstacles by using the cross section data. We see cross section data as spectral measure in polar coordinate at far field. Cross section scattering data suffice to give the local behavior of the wave trace. These local trace formulas contain the geometric information on the obstacle. Local wave trace behavior is connected to the cross section scattering data by Lax-Phillips' formula. Once the scattering data are identical from two different obstacles, the short time behavior of the localized wave trace is expected to give identical heat/wave invariants.

math.AP↗