Related papers: On the stability of the modified entropy equation
We study the stability of multiple almost circular concentrated vortices in a fluid evolving according to the two-dimensional Euler equations. We show that, for general configurations, they must remain concentrated on time-scales much…
Persistent homology and persistent entropy have recently become useful tools for patter recognition. In this paper, we find requirements under which persistent entropy is stable to small perturbations in the input data and scale invariant.…
In this paper, exponential mean-square stability and almost sure stability of the tamed EM scheme to neutral stochastic differential delay equation are investigated. Surprisingly, the exponential mean-square stability can reproduce the…
A nonlinear stochastic differential equation with the order of nonlinearity higher than one, with several discrete and distributed delays and time varying coefficients is considered. It is shown that the sufficient conditions for…
We present an argument for proving the existence of local stable and unstable manifolds in a general abstract setting and under very weak hyperbolicity conditions.
The electronic structure of heavy elements, when described in a space-time which the metric is affected by the electromagnetic interaction, presents instabilities. These instabilities increase with the atomic number, and above a critical…
We prove stability for a coefficient determination problem for a two velocity 2x2 system of hyperbolic PDEs in one space dimension.
A geometric formulation for stabilization of systems with one degree of underactuation which fully solves the energy shaping problem for these system is given. The results show that any linearly controllable simple mechanical system with…
We prove stability bounds for Stokes-like virtual element spaces in two and three dimensions. Such bounds are also instrumental in deriving optimal interpolation estimates. Furthermore, we develop some numerical tests in order to…
In this paper, we consider the exponential stabilization and observation of an unstable heat equation in a general multi-dimensional domain by combining the finite-dimensional spectral truncation technique and the recently developed…
Entropy-stable (ES) schemes have gained considerable attention over the last decade, especially in the context of turbulent flow simulations using high-order methods. While promising because of their nonlinear stability properties, ES…
We use the entropy method to analyze the nonlinear dynamics and stability of a continuum kinetic model of an active nematic suspension. From the time evolution of the relative entropy -- an energy-like quantity in the kinetic model -- we…
A classical model of fluid dynamics is considered which describes the shape evolution of a viscous liquid droplet on a homogeneous substrate. All equilibria are characterized and their stability is analyzed by a geometric reduction…
In this work, we study the slow entropy type invariant of a dynamical system proposed by A. M. Vershik. We provide an explicit construction of a system whose class of scaling entropy sequences is empty. For this unstable case, we introduce…
Curve evolution is often used to solve computer vision problems. If the curve evolution fails to converge, we would not be able to solve the targeted problem in a lifetime. This paper studies the theoretical aspect of the convergence of a…
In this paper, we obtain some stability results of (abstract) dissipative evolution equations with a nonautonomous and nonlinear damping using the exponential stability of the retrograde problem with a linear and autonomous feedback and a…
The stability issue of generalized modified gravitational models is discussed with particular emphasis to de Sitter solutions. Two approaches are briefly presented.
Aim of this paper is to review some basic ideas and recent developments in the theory of strictly hyperbolic systems of conservation laws in one space dimension. The main focus will be on the uniqueness and stability of entropy weak…
This contribution is a follow-up of a recent paper by the authors on adaptive, non-linear time-frequency transforms, focusing on the STFT based transforms. The adaptivity is provided by a focus function, that depends on the analyzed…
The nonlinear filtering equation is said to be stable if it ``forgets'' the initial condition. It is known that the filter might be unstable even if the signal is an ergodic Markov chain. In general, the filtering stability requires…