Related papers: Double exponential stability for generic real-anal…

We construct a family of steady solutions to the two-dimensional incompressible Euler equation in a general bounded domain, such that the vorticity is supported in two well-separated regions of small diameter and converges to a pair of…

We develop a general stability theory for equilibrium points of Poisson dynamical systems and relative equilibria of Hamiltonian systems with symmetries, including several generalisations of the Energy-Casimir and Energy-Momentum methods.…

In this article, we analyze the stability of the parallel surface problem for semilinear equations driven by the fractional Laplacian. We prove a quantitative stability result that goes beyond that previously obtained in [Cir+23]. Moreover,…

A two-dimensional system of differential equations with delay modelling the glucose-insulin interaction processes in the human body is considered. Sufficient conditions are derived for the unique positive equilibrium in the system to be…

We consider the general second order difference equation $x_{n+1}=F(x_n,x_{n-1})$ in which $F$ is continuous and of mixed monotonicity in its arguments. In equations with negative terms, a persistent set can be a proper subset of the…

If $V$ is an irreducible algebraic variety over a number field $K$, and $L$ is a field containing $K$, we say that $V$ is diophantine-stable for $L/K$ if $V(L) = V(K)$. We prove that if $V$ is either a simple abelian variety, or a curve of…

This paper is concerned with the asymptotic stability analysis of a one dimensional wave equation subject to a nonmonotone distributed damping. A well-posedness result is provided together with a precise characterization of the asymptotic…

The paper considers the convergence to equilibrium for measure solutions of the spatially homogeneous Boltzmann equation for hard potentials with angular cutoff. We prove the exponential sharp rate of strong convergence to equilibrium for…

We discuss the stability theory and numerical analysis of the Helmholtz equation with variable and possibly non-smooth or oscillatory coefficients. Using the unique continuation principle and the Fredholm alternative, we first give an…

In this paper, we show for the first time the increasing stability of the inverse source problem for the n-dimensional Helmholtz equation at multiple wave numbers, which is different from the two-or three-dimensional Helmholtz equation. In…

This paper is devoted to the study of nonlinear stability of steady incompressible Euler flows in two dimensions. We prove that a steady Euler flow is nonlinearly stable in $L^p$ norm of the vorticity if its stream function is a semistable…

We prove that any Iterated Function System of circle homeomorphisms with at least one of them having dense orbit, is asymptotically stable. The corresponding Perron-Frobenius operator is shown to satisfy the e-property, that is, for any…

This paper presents a proof that existence of a polynomial Lyapunov function is necessary and sufficient for exponential stability of sufficiently smooth nonlinear ordinary differential equations on bounded sets. The main result states that…

In this paper, we investigate the global exponential stability for complex-valued recurrent neural networks with asynchronous time delays by decomposing complex-valued networks to real and imaginary parts and construct an equivalent…

This work deals with the existence of an almost periodic solution for certain kind of differential equations with generalized piecewise constant argument, almost periodic coefficients which are seen as a perturbation of a linear equation of…

The main objective of this paper is to study the regularity and stability for solutions to the conductivity problems with degenerate coefficients in the presence of two rigid conductors, as one conductor keeps motionless and another…

We prove decay estimates in the interior for solutions to elliptic equations in divergence form with Lipschitz continuous coefficients. The estimates explicitly depend on the distance from the boundary and on suitable notions of frequency…

Asymptotic formula is derived for the behavior of the fundamental solution of the second-order elliptic self-adjoint operator with a piecewise-smooth coefficient in front of the senior derivatives near the discontinuity surface of the…

In this paper, we investigate the quantitative stability for the 2D Couette flow on the infinite channel $\mathbb{R}\times [-1,1]$ with non-slip boundary condition. Compared to the case $\mathbb{T}\times [-1,1]$, we establish the stability…

We consider time-harmonic Maxwell's equations set in an heterogeneous medium with perfectly conducting boundary conditions. Given a divergence-free right-hand side lying in $L^2$, we provide a frequency-explicit approximability estimate…