相关论文: On the backward stability of the second barycentri…

This paper investigates the stability properties of a nonlinear fractional differential equation with two discrete delays and a delay-dependent coefficient. Such equations arise in various biological and control systems where temporal…

The stability of two bubbles rising initially in-line through a viscous liquid is revisited using a global linear stability analysis formulated within an Arbitrary Lagrangian-Eulerian framework, complemented by fully resolved Embedded…

The Lamb-Chaplygin dipole is a traveling wave solution to the 2D incompressible Euler equation, whose orbital stability was established in [Abe-Choi, 2022] and [Abe-Choi-Jeong, 2025] assuming the odd symmetry in $x_2$ (O) and non-negativity…

For solution $u(x,t)$ to degenearte parabolic equations in a bounded domain $\Omega$ with homogenous boundary condition, we consider backward problems in time: determine $u(\cdot,t_0)$ in $\Omega$ by $u(\cdot,T)$, where $t$ is the time…

In this article we consider the stability and damping problem for the 2D Boussinesq equations with partial dissipation near a two parameter family of stationary solutions which includes Couette flow and hydrostatic balance. In the first…

We consider second-order evolution equations in an abstract setting with damping and time delay and give sufficient conditions ensuring exponential stability. Our abstract framework is then applied to the wave equation, the elasticity…

In this paper, we present sharp stability results for various reverse isoperimetric problems in $\mathbb R^2$. Specifically, we prove the stability of the reverse isoperimetric inequality for $\lambda$-convex bodies -- convex bodies with…

In the paper, new estimates of the Lebesgue constant $$ \mathcal{L}(W)=\frac1{(2\pi)^d}\int_{\mathbb{T}^d}\bigg|\sum_{{k}\in W\cap \mathbb{Z}^d} e^{i({k},\,{x})}\bigg| {\rm d}{ x} $$ for convex polyhedra $W\subset\mathbb{R}^d$ are obtained.…

This paper is devoted to the study of secondary resonances and the stability of the Lagrangian point L4 in the spatial restricted three-body problem for moderate mass ratios (mu), meaning that mu is smaller than 0.0045. However, we…

In the Bayesian approach, the a priori knowledge about the input of a mathematical model is described via a probability measure. The joint distribution of the unknown input and the data is then conditioned, using Bayes' formula, giving rise…

For exponents in the subcritical range, we revisit some optimal interpolation inequalities on the sphere with carr\'e du champ methods and use the remainder terms to produce improved inequalities. The method provides us with lower estimates…

We consider Gagliardo-Nirenberg inequalities on the sphere which interpolate between the Poincar\'e inequality and the Sobolev inequality, and include the logarithmic Sobolev inequality as a special case. We establish explicit stability…

In this paper we address the global stability problem for double-bubbles in the plane. This is accomplished by combining the "improved convergence theorem" for planar clusters developed in arXiv:1409.6652 with an ad hoc analysis of the…

In this paper, we review recent results on stability and instability in logarithmic Sobolev inequalities, with a particular emphasis on strong norms. We consider several versions of these inequalities on the Euclidean space, for the…

Here we are investigating the one dimensional inverse source problem for Helmholtz equation where the source function is compactly supported in our domain. We show that increasing stability possible using multi-frequency wave at the two end…

Following the approach of [E1, M1, M2, S1, S2, SZJV] for reaction diffusion systems, we justify rigorously the Eckhaus stability criterion for stability of convective Turing patterns, as derived formally by complex Ginzburg-Landau…

We establish a double logarithmic stability inequality for the problem of determining the initial data in an IBVP for the wave equation outside a non-trapping obstacle from two localized measurements.

Let $\alpha\in (0,2)$, let $${\cal E}(u,u)=\int_{\Bbb R^d}\int_{\Bbb R^d} (u(y)-u(x))^2\frac{A(x,y)}{|x-y|^{d+\alpha}}\, dy\, dx$$ be the Dirichlet form for a stable-like operator, let $$\Gamma u(x)=\int_{\Bbb R^d}…

Using the construction of a Lyapunov function, it is shown that the Douglas-Rachford iteration with respect to a sphere and a line in $\mathbb R^d$ is robustly $\mathcal{KL}$-stable. This implies a convergence which is stronger than uniform…

The profiles of narrow lattice solitons are calculated analytically using perturbation analysis. A stability analysis shows that solitons centered at a lattice (potential) maximum are unstable, as they drift toward the nearest lattice…