Related papers: Logarithmic stability in determining a boundary co…
In this article, high frequency stability estimates for the determination of the potential in the Schr\"odinger equation are studied when the boundary measurements are made on slightly more than half the boundary. The estimates reflect the…
We derive and analyse well-posed boundary conditions for the linear shallow water wave equation. The analysis is based on the energy method and it identifies the number, location and form of the boundary conditions so that the initial…
This paper is concerned with the stability of the inverse boundary value problem for the perturbed fourth-order Schr\"{o}dinger equation in a bounded domain with Cauchy data. We establish stability results for the perturbed potential…
In this paper we present new results on the preservation of polynomial stability of damped wave equations under addition of perturbing terms. We in particular introduce sufficient conditions for the stability of perturbed two-dimensional…
This work belongs to the framework of inverse problems with linear model. The resolution of this type of problem consists in minimizing (possibly under constraints) a function of discrepancy between the measurements and a physical model of…
In this paper we study an inverse boundary value problem for the biharmonic operator with first order perturbation. Our geometric setting is that of a bounded simply connected domain in the Euclidean space of dimension three or higher.…
We consider the problem of determining the unknown boundary values of a solution of an elliptic equation outside a bounded open set $B$ from the knowledge of the values of this solution on a boundary of an arbitrary Lipschitz bounded domain…
In this paper, we shall prove a Carleman estimate for the so-called Zaremba problem. Using some techniques of interpolation and spectral estimates, we deduce a result of stabilization for the wave equation by means of a linear Neumann…
Stability and boundedness analysis for vector nonlinear systems with variable delays and coefficients remains challenging due to the conservatism of existing methods. Moreover, estimates of the transient behavior of solution norms remain…
In this paper, we investigate the stability of the linear wave equation where one part of the boundary, which is seen as a lower-dimensional Riemannian manifold, is governed by a coupled wave equation, while the other part is subject to a…
Understanding how time delays impact the stability of a delay differential equation is important for modeling many natural and technological systems that experience time delays. Here we introduce a new stability criterion for…
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…
We provide a thorough study of stability of the 1-D continuity equation, which models many physical conservation laws. In our system-theoretic perspective, the velocity is considered to be an input. An additional input appears in the…
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…
We deal with the inverse scattering problem of determining the surface impedance of a partially coated obstacle. We prove a stability estimate of logarithmic type for the impedance term by the far field measurements.
Small-signal stability issues-induced broadband oscillations pose significant threats to the secure operation of multi-inverter systems, attracting extensive research attention. Researches revealed that system instability is led by the…
This paper develops 'covariant tomography', a local framework for solving Inverse Boundary Value Problems (IBVP) for parallel transport equation on star-shaped domains. By integrating geometric decomposition with specific interior…
We consider inverse boundary value problems for the Schrodinger equations in two dimensions. Within less regular classes of potentials, we establish a conditional stability estimate of logarithmic order. Moreover we prove the uniqueness…
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…
We study linear damped and viscoelastic wave equations evolving on a bounded domain. For both models, we assume that waves are subject to an inhomogeneous Neumann boundary condition on a portion of the domain's boundary. The analysis of…