Related papers: Exponential instability in the Gel'fand inverse pr…
We study stability times for a family of parameter dependent nonlinear Schr\"odinger equations on the circle, close to the origin. Imposing a suitable Diophantine condition (first introduced by Bourgain), we prove a rather flexible Birkhoff…
The oscillation of a Laplacian eigenfunction gives a great deal of information about the manifold on which it is defined. This oscillation can be encoded in the nodal deficiency, an important geometric quantity that is notoriously hard to…
The stability of five finite difference-time domain (FD-TD) schemes coupling Maxwell equations to Debye or Lorentz models have been analyzed in [1] (P.G. Petropoulos, "Stability and phase error analysis of FD-TD in dispersive dielectrics",…
This paper is devoted to the inverse problem of recovering simultaneously a potential and a point source in a Shr\"odinger equation from the associated nonlinear Dirichlet to Neumann map. The uniqueness of the inversion is proved and…
In this paper we are interested in establishing stability estimates in the inverse problem of determining on a compact Riemannian manifold the electric potential or the conformal factor in a Schr\"odinger equation with Dirichlet data from…
We discuss the inverse problem of determining the, possibly anisotropic, conductivity of a body $\Omega\subset\mathbb{R}^{n}$ when the so--called Dirichlet-to-Neumann map is locally given on a non empty portion $\Gamma$ of the boundary…
This paper investigates instability ranges of a cylindrically symmetric collapsing stellar object in Brans-Dicke theory of gravity. For this purpose, we use perturbation approach in the modified field equations as well as dynamical…
In this paper, we investigate the asymptotic behaviors of the solutions of nonlinear dynamic systems nearby an equilibrium point, when the nominal parts are subject to non necessarily small perturbations. We show that, under some estimates…
In this paper, the uniform stability of the inverse spectral problem is proved for the matrix Sturm-Liouville operator on a finite interval. Namely, we describe the sets of spectral data, on which the inverse spectral mapping is bounded…
In this article, we discuss stability of the one-dimensional overdamped Lange\-vin equation in double-well potential. We determine unstable and stable equilibria, and discuss the rate of convergence to stable ones. Also, we derive…
This study considers the stability of a non-inflectional elastica under a conservative end force subject to the Dirichlet, mixed, and Neumann boundary conditions. It is demonstrated that the non-inflectional elastica subject to the…
We study the stability in the inverse problem of determining the time dependent zeroth-order coefficient $q(t,x)$ arising in the wave equation, from boundary observations. We derive, in dimension $n\geq 2$, a log-type stability estimate in…
We consider the existence and uniqueness of a minimizer of the extremal problem for weighted combined energy between two concentric annuli and obtain that the extremal mapping is a certain radial mapping. Meanwhile, this in turn implies a…
We deal with the problem of determining a time varying inclusion within a thermal conductor. In particular we study the continuous dependance of the inclusion from the Dirichlet-to-Neumann map. Under a priori regularity assumptions on the…
We establish (i) stability of Lyapunov exponents and (ii) convergence in probability of Oseledets spaces for semi-invertible matrix cocycles, subjected to small random perturbations. The first part extends results of Ledrappier and Young to…
We consider inverse problems for $p$-Laplace type equations under monotonicity assumptions. In two dimensions, we show that any two conductivities satisfying $\sigma_1 \geq \sigma_2$ and having the same nonlinear Dirichlet-to-Neumann map…
We obtain the instability of Type (II) Lawson-Osserman cones in Euclidean spaces, and thus provide a family of (uncountably many) unstable solutions with singularity to the Dirichlet problem for minimal graphs of high codimension versus…
For the 2D incompressible Euler equations, we establish global-in-time ($t \in \mathbb{R}$) stability of vortex quadrupoles satisfying odd symmetry with respect to both axes. Specifically, if the vorticity restricted to a quadrant is…
We study spectral stability estimates of elliptic operators in divergence form $-\textrm{div} [A(w) \nabla g(w)]$ with the Dirichlet boundary condition in non-Lipschitz domains $\widetilde{\Omega} \subset \mathbb C$. The suggested method is…
Using the energy method we investigate the stability of pure conduction in Pearson's model for B\'enard-Marangoni convection in a layer of fluid at infinite Prandtl number. Upon extending the space of admissible perturbations to the…