23 citations · 70 across the 19 of their papers we have counts for
21 papers
On elastic scattering behavior of corner domains
Pu-Zhao Kow, Mikko Salo, Henrik Shahgholian
We investigate the scattering of elastic waves by anisotropic inhomogeneous media at a fixed wave number. We prove that, in two dimensions, every penetrable obstacle with piecewise…
Multiphase quadrature domains (existence and uniqueness)
Pu-Zhao Kow, Henrik Shahgholian, Tomas Sjödin
The primary goal of this paper is to give a precise definition and prove existence and uniqueness of multiphase quadrature domains for subharmonic functions, ensuring that the pres…
Inverse problems for the spectral fractional Laplacian with inhomogeneous Dirichlet boundary data
Ravi Shankar Jaiswal, Pu-Zhao Kow, Suman Kumar Sahoo
In this paper, we study the spectral fractional Laplacian with inhomogeneous Dirichlet boundary data. Our contributions are twofold: first we introduce a Dirichlet-to-Neumann map f…
Existence and regularity of minimizers for a variational problem of species population density
Pu-Zhao Kow, Masato Kimura, Hiroshi Ohtsuka
We study a variational problem motivated by models of species population density in a nonhomogeneous environment. We first analyze local minimizers and the structure of the saturat…
On scattering behavior of corner domains with anisotropic inhomogeneities: part II
Pu-Zhao Kow, Mikko Salo, Henrik Shahgholian
We study the scattering behavior of an anisotropic inhomogeneous Lipschitz medium at a fixed wave number, continuing our previous work [SIAM J. Math. Anal., 56(4):4834-4853, 2024]…
Bayesian inference for the fractional Calderón problem with a single measurement
Pu-Zhao Kow, Janne Nurminen, Jesse Railo
This paper investigates the consistency of a posterior distribution in the single-measurement fractional Calderón problem with additive Gaussian noise. We consider a Bayesian frame…
An inverse problem for semilinear elliptic equations with generalized Kerr-type nonlinearities
Pu-Zhao Kow, Rulin Kuan
We study the inverse problem of reconstructing the convex hull of unknown inclusions in semilinear elliptic equations with nonanalytic nonlinearities, by extending Ikehata's enclos…
A Speech Enhancement Method Using Fast Fourier Transform and Convolutional Autoencoder
Pu-Yun Kow, Pu-Zhao Kow
This paper addresses the reconstruction of audio signals from degraded measurements. We propose a lightweight model that combines the discrete Fourier transform with a Convolutiona…
Increasing resolution and instability for linear inverse scattering problems
Pu-Zhao Kow, Mikko Salo, Sen Zou
In this work we study the increasing resolution of linear inverse scattering problems at a large fixed frequency. We consider the problem of recovering the density of a Herglotz wa…
Multi-phase -quadrature domains and applications to acoustic waves and magnetic fields
Pu-Zhao Kow, Henrik Shahgholian
The primary objective of this paper is to explore the multi-phase variant of quadrature domains associated with the Helmholtz equation, commonly referred to as -quadrature domai…
On scattering behavior of corner domains with anisotropic inhomogeneities
Pu-Zhao Kow, Mikko Salo, Henrik Shahgholian
This paper investigates the possible scattering and non-scattering behavior of an anisotropic and inhomogeneous Lipschitz medium at a fixed wave number and with a single incident f…
Unique continuation for the momentum ray transform
Joonas Ilmavirta, Pu-Zhao Kow, Suman Kumar Sahoo
The present article focuses on a unique continuation result for certain weighted ray transforms, utilizing the unique continuation property (UCP) of the fractional Laplace operator…
A minimization problem with free boundary and its application to inverse scattering problems
Pu-Zhao Kow, Mikko Salo, Henrik Shahgholian
We study a minimization problem with free boundary, resulting in hybrid quadrature domains for the Helmholtz equation, as well as some application to inverse scattering problem.
On positivity sets for Helmholtz solutions
Pu-Zhao Kow, Mikko Salo, Henrik Shahgholian
We address the question of finding global solutions of the Helmholtz equation that are positive in a given set. This question arises in inverse scattering for penetrable obstacles.…
Quadrature domains for the Helmholtz equation with applications to non-scattering phenomena
Pu-Zhao Kow, Simon Larson, Mikko Salo +1
In this paper, we introduce quadrature domains for the Helmholtz equation. We show existence results for such domains and implement the so-called partial balayage procedure. We als…
An inverse problem for semilinear equations involving the fractional Laplacian
Pu-Zhao Kow, Shiqi Ma, Suman Kumar Sahoo
Our work concerns the study of inverse problems of heat and wave equations involving the fractional Laplacian operator with zeroth order nonlinear perturbations. We recover nonline…
Landis-type conjecture for the half-Laplacian
Pu-Zhao Kow, Jenn-Nan Wang
In this paper, we study the Landis-type conjecture, i.e., unique continuation property from infinity, of the fractional Schrödinger equation with drift and potential terms. We show…
The Calderón problem for the fractional wave equation: Uniqueness and optimal stability
Pu-Zhao Kow, Yi-Hsuan Lin, Jenn-Nan Wang
We study an inverse problem for the fractional wave equation with a potential by the measurement taking on arbitrary subsets of the exterior in the space-time domain. We are intere…
Optimality of increasing stability for an inverse boundary value problem
Pu-Zhao Kow, Gunther Uhlmann, Jenn-Nan Wang
In this work we study the optimality of increasing stability of the inverse boundary value problem (IBVP) for Schrödinger equation. The rigorous justification of increasing stabili…
The Lewy-Stampacchia Inequality for the Fractional Laplacian and Its Application to Anomalous Unidirectional Diffusion Equations
Pu-Zhao Kow, Masato Kimura
In this paper, we consider a Lewy-Stampacchia-type inequality for the fractional Laplacian on a bounded domain in Euclidean space. Using this inequality, we can show the well-posed…
On Landis Conjecture for the Fractional Schrödinger Equation
Pu-Zhao Kow
In this paper, we study a Landis-type conjecture for the general fractional Schrödinger equation . As a byproduct, we also proved the additivity and boundedness of…