Related papers: An inverse hyperbolic obstacle problem
For the quermassintegral inequalities of horospherically convex hypersurfaces in the $(n+1)$-dimensional hyperbolic space, where $n\geq 2$, we prove a stability estimate relating the Hausdorff distance to a geodesic sphere by the deficit in…
Under consideration are mathematical models of heat and mass transfer. We study inverse problems of recovering lower-order coefficients in a second order parabolic equation. The coefficients are representable in the form of a finite…
This paper studies a prototype of inverse obstacle scattering problems whose governing equation is the Helmholtz equation in two dimensions. An explicit method to extract information about the location and shape of unknown obstacles from…
The solution of a multi-frequency 1d inverse medium problem consists of recovering the refractive index of a medium from measurements of the scattered waves for multiple frequencies. In this paper, rigorous stability estimates are derived…
In this Note, we review the main existing results, methods, and some key open problems on the controllability of nonlinear hyperbolic and parabolic equations. Especially, we describe our recent universal approach to solve the local…
Stabilization of a coupled system consisting of a parabolic partial differential equation and an elliptic partial differential equation is considered. Even in the situation when the parabolic equation is exponentially stable on its own, the…
The problem of reconstruction of an unknown refractive index $k(x)$ of an inhomogeneous solid $P$ is considered. The refractive index is assumed to be a piecewise-H\"{o}lder function The original boundary value problem for the Helmholtz…
In this work, we shall study the nonlinear inverse problems of recovering the Robin coefficients in elliptic and parabolic systems of second order, and establish their local Lipschitz stabilities. Some local Lipschitz stability was derived…
We are interested in the feedback stabilization of systems described by Hamilton-Jacobi type equations in $\mathbb{R}^n$. A reformulation leads to a a stabilization problem for a multi-dimensional system of $n$ hyperbolic partial…
This paper presents a theoretical and numerical investigation of object detection in a fluid governed by the three-dimensional evolutionary Navier--Stokes equations. To solve this inverse problem, we assume that interior velocity…
We initiate studying inverse spectral problems for Dirac-type functional-differential operators with constant delay. For simplicity, we restrict ourselves to the case when the delay parameter is not less than one half of the interval. For…
We consider the problem of identifying discontinuous doping profiles in semiconductor devices from data obtained by different models connected to the voltage-current map. Stationary as well as transient settings are discussed and a…
Now a final and maybe simplest formulation of the enclosure method applied to inverse obstacle problems governed by partial differential equations in a {\it spacial domain with an outer boundary} over a finite time interval is fixed. The…
In this paper, we consider a moving rigid solid immersed in a potential fluid. The fluid-solid system fills the whole two dimensional space and the fluid is assumed to be at rest at infinity. Our aim is to study the inverse problem,…
A stability version of the reverse isoperimetric inequality, and the corresponding inequality for isotropic measures are established.
We study the inverse problem in Optical Tomography of determining the optical properties of a medium $\Omega\subset\mathbb{R}^n$, with $n\geq 3$, under the so-called diffusion approximation. We consider the time-harmonic case where $\Omega$…
In this paper we improve the approach of a previous paper about the domino problem in the hyperbolic plane, see arXiv.cs.CG/0603093. This time, we prove that the general problem of the hyperbolic plane with \`a la Wang tiles is undecidable.
Thermoacoustic tomography is a term for the inverse problem of determining of one of initial conditions of a hyperbolic equation from boundary measurements. In the past publications both stability estimates and convergent numerical methods…
Inverse design of morphing slender structures with programmable curvature has significant applications in various engineering fields. Most existing studies formulate it as an optimization problem, which requires repeatedly solving the…
The global equi-continuity estimate on Lp-viscosity solutions of bilateral obstacle problems with unbounded ingredients is established when obstacles are merely continuous. The existence of Lp-viscosity solutions is established via an…