63 citations · 640 across the 59 of their papers we have counts for
58 papers · 1 filter
Removing small wavenumber constraints in Side B of the Probe Method
Masaru Ikehata
The Probe Method is an analytical reconstruction scheme for inverse obstacle problems utilizing the Dirichlet-to-Neumann map associated with the governing partial differential equa…
Integrating the probe and singular sources methods: IV. IPS function for the Schrödinger equation
Masaru Ikehata
The integrated theory of the probe and singular sources methods (IPS) is developed for an inverse obstacle problem governed by the stationary Schrödinger equation in a bounded doma…
Integrating the probe and singular sources methods: III. Mixed obstacle case
Masaru Ikehata
The main purpose of this paper is to develop further the integrated theory of the probe and singular sources methods (IPS) which may work for a group of inverse obstacle problems.…
Integrating the probe and singular sources methods :II. The Stokes system
Masaru Ikehata
In this paper, an integrated theory of the probe and singular sources methods for an inverse obstacle problem governed by the Stokes system in a bounded domain is developed. The ma…
Integrating the probe and singular sources methods
Masaru Ikehata
The probe and singular sources methods are two well-known classical direct reconstruction methods in inverse obstacle problems governed by partial differential equations. In this p…
Remarks on the paper: Ikehata, M., Extraction formulae for an inverse boundary value problem for the equation , Inverse Problems, 18(2002), 1281-1290
Masaru Ikehata
Some remarks on the jump condition appearing in Theorems 1.1 and 1.2 in the article [1] and their implications are given.
On extracting the positions of multiple unknown cracks that occur on the junction line of two elastic plates
Masaru Ikehata, Hiromichi Itou
This paper is concerned with the reconstruction issue of an inverse crack problem in a two-dimensional bounded domain which may have a possible application to the nondestructive ev…
The enclosure method for the detection of variable order in fractional diffusion equations
Masaru Ikehata, Yavar Kian
This paper is concerned with a new type of inverse obstacle problem governed by a variable-order time-fraction diffusion equation in a bounded domain. The unknown obstacle is a reg…
Revisiting the probe and enclosure methods
Masaru Ikehata
This paper is concerned with reconstruction issue of inverse obstacle problems governed by partial differential equations and consists of two parts. (i) The first part considers th…
An approach based on the wave equation in the time domain for active shielding of an unwanted wave with a fixed frequency
Masaru Ikehata
An approach for shielding an unwanted wave with a fixed frequency by generating a suitably controlled nontrivial wave with the same frequency is suggested. Unlike the well known su…
Reconstruction of a source domain from the Cauchy data: II. Three dimensional case
Masaru Ikehata
This paper is concerned with reconstruction issue of some typical inverse problems and consists of three parts. First a framework of the enclosure method for an inverse source prob…
On finding a penetrable obstacle using a single electromagnetic wave in the time domain
Masaru Ikehata
The time domain enclosure method is one of analytical methods for inverse obstacle problems governed by partial differential equations in the time domain. This paper considers the…
The enclosure method using a single point on the graph of the response operator for the Stokes system
Masaru Ikehata
An inverse obstacle problem governed by the Stokes system in the time domain is considered. Two types of extraction formulae about the geometry of an unknown obstacle are given by…
Extracting discontinuity using the probe and enclosure methods
Masaru Ikehata
This is a review article on the development of the probe and enclosure methods from past to present, focused on their central ideas together with various applications.
The Herglotz wave function, the Vekua transform and the enclosure method
Masaru Ikehata
This paper gives applications of the enclosure method introduced by the author to typical inverse obstacle and crack scattering problems in two dimensions. Explicit extraction form…
A new formulation of the probe method and related problems
Masaru Ikehata
The probe method gives a general idea to obtain a reconstruction formula of unknown objects embedded in a known background medium from a mathematical counterpart (the Dirichlet-to-…
On uniqueness in the inverse obstacle problem via the positive supersolutions of the Helmholtz equation
Masaru Ikehata
This paper is concerned with an inverse obstacle scattering problem of an acoustic wave for a single incident plane wave and a wave number. The Colton-Sleeman theorem states the un…
The enclosure method for inverse obstacle scattering over a finite time interval: VI. Using shell type initial data
Masaru Ikehata
A simple idea of finding a domain that encloses an unknown discontinuity embedded in a body is introduced by considering an inverse boundary value problem for the heat equation. Th…
Remarks on Lin-Nakamura-Wang's paper
Masaru Ikehata
Theorem 1.2 in their paper arXiv:1904.00999v1 [math.AP] 30 Mar 2019 "Reconstruction of unknown cavity by single measurement" is not valid.
On reconstruction from a partial knowledge of the Neumann-to-Dirichlet operator
Masaru Ikehata
We give formulae that yield an information about the location of an unknown polygonal inclusion having unknown constant conductivity inside a known conductive material having known…
On reconstruction in the inverse conductivity problem with one measurement
Masaru Ikehata
We consider an inverse problem for electrically conductive material occupying a domain in . Let be the conductivity of , and a subdomain of . We assume…
Extraction formulae for an inverse boundary value problem for the equation
Masaru Ikehata
We consider an inverse boundary value problem for the equation in a given bounded domain at a fixed . and denote the conductivity an…
A study on finding a buried obstacle in a layered medium having the influence of the total reflection phenomena via the time domain enclosure method
Masaru Ikehata, Mishio Kawashita, Wakako Kawashita
An inverse obstacle problem for the wave governed by the wave equation in a two layered medium is considered under the framework of the time domain enclosure method. The wave is ge…
Revealing cracks inside conductive bodies by electric surface measurements
Andreas Hauptmann, Masaru Ikehata, Hiromichi Itou +1
An algorithm is introduced for using electrical surface measurements to detect and monitor cracks inside a two-dimensional conductive body. The technique is based on transforming t…