It is proved that one can choose a control function on an arbitrarilly small open subset of the boundary of an obstacle so that the total radiation from this obstacle for a fixed direction of the incident plane wave and for a fixed wave number will be as small as one wishes. The obstacle is called "invisible" in this case.

Let $y\left(h\right)(t,x)$ be one solution to$${\partial }_{t}y(t,x)-\sum _{i,j=1}^n{\partial }_j\left(a_{ij}\left(x\right){\partial }_{i}y(t,x)\right)=h(t,x),0\<t\<T,x\in \Omega$$with a non-homogeneous term $h$, and ${y|}_{(0,T)\times \partial \Omega }=0$, where $\Omega \subset {ℝ}^n$ is a bounded domain. We discuss an inverse problem of determining $n(n+1)/2$ unknown functions $a_{ij}$ by $\{{\partial }_{\nu }y\left(h_{\ell }\right){|}_{(0,T)\times {\Gamma }_0}$, $y\left(h_{\ell }\right)(\theta ,·){\}}_{1\le \ell \le {\ell }_0}$ after selecting input sources $h_1,...,h_{{\ell }_0}$ suitably, where ${\Gamma }_0$ is an arbitrary subboundary, ${\partial }_{\nu }$ denotes the normal derivative, $0\<\theta \<T$ and ${\ell }_0\in \mathbb{N}$. In the case of ${\ell }_0={(n+1)}^{2}n/2$, we prove the Lipschitz stability in the inverse problem if we choose $(h_1,...,h_{{\ell }_0})$ from a set $\mathscr{H}\subset {\left\{C_0^{\infty }((0,T)\times \omega )\right\}}^{{\ell }_0}$ with an arbitrarily fixed subdomain $\omega \subset \Omega$. Moreover we can take ${\ell }_0=(n+3)n/2$ by making special choices for $h_{\ell }$, $1\le \ell \le {\ell }_0$. The proof is...

Let y(h)(t,x) be one solution to $${\partial }_{t}y(t,x)-\sum _{i,j=1}^n{\partial }_j\left(a_{ij}\left(x\right){\partial }_{i}y(t,x)\right)=h(t,x),0<t<T,x\in \Omega$$ with a non-homogeneous term h, and ${y|}_{(0,T)\times \partial \Omega }=0$, where $\Omega \subset {ℝ}^n$ is a bounded domain. We discuss an inverse problem of determining n(n+1)/2 unknown functions aij by $\{{\partial }_{\nu }y\left(h_{\ell }\right){|}_{(0,T)\times {\Gamma }_0}$, $y\left(h_{\ell }\right)(\theta ,·){\}}_{1\le \ell \le {\ell }_0}$ after selecting input sources $h_1,...,h_{{\ell }_0}$ suitably, where ${\Gamma }_0$ is an arbitrary subboundary, ${\partial }_{\nu }$ denotes the normal derivative, $0<\theta <T$ and ${\ell }_0\in \mathbb{N}$. In the case of ${\ell }_0={(n+1)}^{2}n/2$, we prove the Lipschitz stability in the inverse problem if we choose $(h_1,...,h_{{\ell }_0})$ from a set $\mathscr{H}\subset {\left\{C_0^{\infty }((0,T)\times \omega )\right\}}^{{\ell }_0}$ with an arbitrarily fixed subdomain $\omega \subset \Omega$. Moreover we can take ${\ell }_0=(n+3)n/2$ by making special choices for...

Electro-muscular disruption (EMD) devices such as TASER M26 and X26 have been used as a less-than-lethal weapon. Such EMD devices shoot a pair of darts toward an intended target to generate an incapacitating electrical shock. In the use of the EMD device, there have been controversial questions about its safety and effectiveness. To address these questions, we need to investigate the distribution of the current density J inside the target produced by the EMD device. One approach is to develop a computational...

We study certain Fourier integral operators arising in the inversion of data from reflection seismology.

We first prove an abstract result for a class of nonlocal problems using fixed point method. We apply this result to equations revelant from plasma physic problems. These equations contain terms like monotone or relative rearrangement of functions. So, we start the approximation study by using finite element to discretize this nonstandard quantities. We end the paper by giving a numerical resolution of a model containing those terms.

In the article the following optimal control problem is studied: to determine a certain coefficient in a quasilinear partial differential equation of parabolic type so that the solution of a boundary value problem for this equation would minimise a given integral functional. In addition to the design and analysis of a numerical method the paper contains the solution of the fundamental problems connected with the formulation of the problem in question (existence and uniqueness of the solution of...

The Bayesian inversion is a natural approach to the solution of inverse problems based on uncertain observed data. The result of such an inverse problem is the posterior distribution of unknown parameters. This paper deals with the numerical realization of the Bayesian inversion focusing on problems governed by computationally expensive forward models such as numerical solutions of partial differential equations. Samples from the posterior distribution are generated using the Markov chain Monte...

We consider the numerical solution, in two- and three-dimensional bounded domains, of the inverse problem for identifying the location of small-volume, conductivity imperfections in a medium with homogeneous background. A dynamic approach, based on the wave equation, permits us to treat the important case of “limited-view” data. Our numerical algorithm is based on the coupling of a finite element solution of the wave equation, an exact controllability method and finally a Fourier inversion for localizing...

We consider the numerical solution, in two- and three-dimensional bounded domains, of the inverse problem for identifying the location of small-volume, conductivity imperfections in a medium with homogeneous background. A dynamic approach, based on the wave equation, permits us to treat the important case of “limited-view” data. Our numerical algorithm is based on the coupling of a finite element solution of the wave equation, an exact controllability method and finally a Fourier inversion for...