Related papers: Increasing stability for near field from the scatt…
This paper is concerned with the stability estimates for inverse source problems of the stochastic Helmholtz equation driven by white noise. The well-posedness is established for the direct source problems, which ensures the existence and…
The creation and justification of the methods for minimax estimation of parameters of the external boundary value problems for the Helmholtz equation in unbounded domains are considered. When observations are distributed in subdomains, the…
The scattering of quasiperiodic waves for a two-dimensional Helmholtz equation with a constant refractive index perturbed by a function which is periodic in one direction and of finite support in the other is considered. The scattering…
This paper is devoted to the exponential stability for one-dimensional linear wave equations with in-domain localized damping and several types of Wentzell (or dynamic) boundary conditions. In a quite general boundary setting, we establish…
We consider the multi-frequency inverse source problem in the presence of a non-homogeneous medium using passive measurements. Precisely, we derive stability estimates for determining the source from the knowledge of only the imaginary part…
We extend Loeper's $L^2$-estimate relating the electric fields to the densities for the Vlasov-Poisson system to $L^p$, with $1 < p < +\infty$, based on the Helmholtz-Weyl decomposition. This allows us to generalize both the classical…
We investigate the stability of the wave equation with spatial dependent coefficients on a bounded multidimensional domain. The system is stabilized via a scattering passive feedback law. We formulate the wave equation in a port-Hamiltonian…
We develop here the method for obtaining approximate stability boundaries in the space of parameters for systems with parametric excitation. The monodromy (Floquet) matrix of linearized system is found by averaging method. For system with 2…
This paper is concerned with the inverse problem to recover the scalar, complex-valued refractive index of a medium from measurements of scattered time-harmonic electromagnetic waves at a fixed frequency. The main results are two…
We establish stability inequalities for the problem of determining the potential, appearing in a Sch\"odinger equation, from partial boundary data in the high frequency limit. These stability inequalities hold under the assumption that the…
In this paper, we consider the stabilization of wave equations with moving boundary. First, we show the solution behaviour of wave equation with Neumann boundary conditions, that is, the energy of wave equation with mixed boundary…
Pattern formation in systems with a conserved quantity is considered by studying the appropriate amplitude equations. The conservation law leads to a large-scale neutral mode that must be included in the asymptotic analysis for pattern…
In this paper, we show the increasing stability of the inverse source problems for the acoustic wave equation in the full space R3.The goal is to understand increasing stability for wave equation in the time domain. If the time and spatial…
The goal of this paper is to show that evanescent plane waves are much better at numerically approximating Helmholtz solutions than classical propagative plane waves. By generalizing the Jacobi$\unicode{x2013}$Anger identity to…
This paper is concerned with the stability of the inverse source problem for the damped biharmonic plate equation in three dimensions. The stability estimate consists of the Lipschitz type data discrepancy and the high frequency tail of the…
For the problem of diffraction of harmonic scalar waves by a lossless periodic slab scatterer, we analyze field sensitivity with respect to the material coefficients of the slab. The governing equation is the Helmholtz equation, which…
A two-dimensional model of an electron moving under the influence of an attractive zero-range potential as well as external magnetic and electric fields is analyzed. We prove by numerical investigations that there are formed such resonances…
We discuss the analysis and stability of a family of cross-diffusion boundary value problems with nonlinear diffusion and drift terms. We assume that these systems are close, in a suitable sense, to a set of decoupled and linear problems.…
We prove stability estimates for the problem of recovering the nonlinearity from scattering data. We focus our attention on nonlinear Schr\"odinger equations of the form \[ (i\partial_t+\Delta)u = a(x)|u|^p u \] in three space dimensions,…
Exact solutions describing the Rayleigh-Bloch waves for the two-dimensional Helmholtz equation are constructed in the case when the refractive index is a sum of a constant and a small amplitude function which is periodic in one direction…