相关论文: Logarithmic stability in determining two coefficie…

In [2] we introduced a method combining together an observability inequality and a spectral decomposition to get a logarithmic stability estimate for the inverse problem of determining both the potential and the damping coefficient in a…

We are concerned with the problem of determining the damping boundary coefficient appearing in a dissipative wave equation from a single boundary measurement. We prove that the uniqueness holds at the origin provided that the initial…

We improve the preceding results obtained by the first and the second authors in [3]. They concern the stability issue of the inverse problem that consists in determining the potential and the damping coefficient in a wave equation from an…

We prove a logarithmic stability estimate for the inverse problem of determining the potential in a wave equation from boundary measurements obtained by varying the first component of the initial condition. The novelty of the present work…

We prove logarithmic stability in the parabolic inverse problem of determining the space-varying factor in the source, by a single partial boundary measurement of the solution to the heat equation in an infinite closed waveguide, with…

In this paper, the vibration model of an elastic beam, governed by the damped Euler-Bernoulli equation $\rho(x)u_{tt}+\mu(x)u_{t}$$+\left(r(x)u_{xx}\right)_{xx}=0$, subject to the clamped boundary conditions $u(0,t)=u_x(0,t)=0$ at $x=0$,…

In this paper we study the controllability and the stability for a degenerate beam equation in divergence form via the energy method. The equation is clamped at the left end and controlled by applying a shearing force or a damping at the…

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…

This paper investigates the identification of two coefficients in a coupled hyperbolic system with an observation on one component of the solution. Based on the the Carleman estimate for coupled wave equations a logarithmic type stability…

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…

This paper is addressed to a stabilization problem of a system coupled by a wave and a Euler-Bernoulli plate equation. Only one equation is supposed to be damped. Under some assumption about the damping and the coupling terms, it is shown…

In this paper, we treat the inverse problem of determining two time-dependent coefficients appearing in a dissipative wave equation, from measured Neumann boundary observations. We establish in dimension $n\geq 2$, stability estimates with…

We consider an initial and boundary value problem the one dimensional wave equation with damping concentrated at an interior point. We prove a result of a logarithmic decay of the energy of a system with homogeneous Dirichlet boundary…

We consider the stability in the inverse problem consisting in the determination of an electric potential $q$, appearing in a Dirichlet initial-boundary value problem for the wave equation $\partial_t^2u-\Delta u+q(x)u=0$ in an unbounded…

This paper establishes Lipschitz stability for the simultaneous recovery of a variable density coefficient and the initial displacement in a damped biharmonic wave equation. The data consist of the boundary Cauchy data for the Laplacian of…

In this paper, we consider an Euler-Bernoulli beam equation with time-varying internal fluid. We assume that the fluid is moving with non-constant velocity and dynamical boundary conditions are satisfied. We prove the existence and…

This paper explores the exponential stability of two nonlinear wave equations coupled through their velocities. The analysis is divided into two main cases. First, we consider a system where one equation is damped, while the other…

This paper is concerned with the decay estimate of solutions to the semilinear wave equation subject to two localized dampings in a bounded domain. The first one is of the nonlinear Kelvin-Voigt type and is distributed around a neighborhood…

In this paper we prove stability estimates of logarithmic type for an inverse problem consisting in the determination of unknown portions of the boundary of a domain in $\mathbb{R}^n$, from a knowledge, in a finite time observation, of…

As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…