Related papers: Global stability for a coupled physics inverse pro…
In this paper, we present a refined approach to establish a global Lipschitz stability for an inverse source problem concerning the determination of forcing terms in the wave equation with mixed boundary conditions. It consists of boundary…
The problem of a particle of mass m in the field of the inverse square potential is studied in quantum mechanics with a generalized uncertainty principle, characterized by the existence of a minimal length. Using the coordinate…
In this paper we present a proof of the orbital stability of ground state for logarithmic Schr\"odinger equation in any dimension and under nonradial perturbations.
We prove stability for a formally determined inverse problem for a hyperbolic PDE where the coefficients depend on space and time variables. The hyperbolic operator has constant wave speed and we study the recovery of zeroth order and first…
The purpose of this note is to prove global-in-time smoothing effects for the Schr\"odinger equation with potentials exhibiting critical singularity. A typical example of admissible potentials is the inverse-square potential $a|x|^{-2}$…
We prove the nonlinear stability of the Schwarzschild spacetime under axially symmetric polarized perturbations, i.e. solutions of the Einstein vacuum equations for asymptotically flat $1+3$ dimensional Lorentzian metrics which admit a…
In this paper, we for the first time prove local solvability and stability of the inverse Sturm-Liouville problem with complex-valued singular potential and with polynomials of the spectral parameter in the boundary conditions. The proof…
We prove definitive results on the global stability of the flat space among solutions of the Einstein-Klein-Gordon system. Our main theorems in this monograph include: (1) A proof of global regularity (in wave coordinates) of solutions of…
In this paper we address the global stability problem for double-bubbles in the plane. This is accomplished by combining the "improved convergence theorem" for planar clusters developed in arXiv:1409.6652 with an ad hoc analysis of the…
We prove global existence for Einstein's equations with a charged scalar field for initial conditions sufficiently close to the Minkowski spacetime without matter. The proof relies on generalized wave coordinates adapted to the outgoing…
We give an instability estimate for the Gel'fand inverse boundary value problem at high energies. Our instability estimate shows an optimality of several important preceeding stability results on inverse problems of such a type.
This paper is concerned with an inverse source problem for the three-dimensional Helmholtz equation by a single boundary measurement at a fixed frequency. We show the Lipschitz stability under the assumption that the source function is…
For linearized Navier-Stokes equations, we consider an inverse source problem of determining a spatially varying divergence-free factor. We prove the global Lipschitz stability by interior data over a time interval and velocity field at…
In this paper, we study the stability of the inverse conductivity problem of determining a convex polyhedral inclusion embedded in a homogeneous isotropic medium from a single boundary measurement. The main tools in our analysis are…
We are interested in the identification of a Generalized Impedance Boundary Condition from the far--fields created by one or several incident plane waves at a fixed frequency. We focus on the particular case where this boundary condition is…
We consider the problem of global stability of solutions to a class of semilinear wave equations with null condition in Minkowski space. We give sufficient conditions on the given solution which guarantees stability. Our stability result…
We study the recovery of a spatially dependent source in a one-dimensional space-time fractional wave equation using boundary measurement data collected at a single endpoint. The main challenge arises from the fact that the eigenfunctions…
In this paper, we will study increasing stability in the inverse source problem for the Helmholtz equation in the plane when the source term is assumed to be compactly supported in a bounded domain $\Omega$ with sufficiently smooth…
This result will be published as part of my PhD thesis after some streamlining. This manuscript contains the proof of the claim, but is not peer-reviewed. We prove uniqueness and stability for the inverse problem of the 2D Schr\"odinger…
The inverse problem of backward diffusion is known to be ill-posed and highly unstable. Backward diffusion processes appear naturally in image enhancement and deblurring applications. It is therefore greatly desirable to establish a…