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We consider a modified Ricci flow equation whose stationary solutions include Einstein and Ricci soliton metrics, and we study the linear stability of those solutions relative to the flow. After deriving various criteria that imply linear…
We prove a stability result of constant equilibria for the three-dimensional Navier-Stokes-Poisson system uniform in the inviscid limit. We allow the initial density to be close to a constant and the potential part of the initial velocity…
We investigate the stability of electrodeposition at solid-solid interfaces for materials exhibiting an anisotropic mechanical response. The stability of electrodeposition or resistance to the formation of dendrites is studied within a…
We study certain significant properties of the equilibrium configurations of a rigid body subject to an undamped elastic restoring force, in the stream of a viscous liquid in an unbounded 3D domain. The motion of the coupled system is…
To improve detection robustness in adverse conditions (e.g., haze and low light), image restoration is commonly applied as a pre-processing step to enhance image quality for the detector. However, the functional mismatch between restoration…
We consider the inverse boundary value problem of determining the potential $q$ in the equation $\Delta u + qu = 0$ in $\Omega\subset\mathbb{R}^n$, from local Cauchy data. A result of global Lipschitz stability is obtained in dimension…
We obtain free of resonances regions for the elasticity system in the exterior of a strictly convex body with dissipative boundary conditions under some natural assumptions on the behaviour of the geodesics on the boundary.
We study the boundary rigidity problem for compact Riemannian manifolds with boundary $(M,g)$: is the Riemannian metric $g$ uniquely determined, up to an action of diffeomorphism fixing the boundary, by the distance function $\rho_g(x,y)$…
This paper focuses on using curvature and torsion to describe the stability of linear time-invariant system. We prove that for a two-dimensional system $\dot{r}(t)= Ar(t)$, (i) if there exists an initial value, such that zero is not the…
In this paper we introduce the notion of rigidity for harmonic-Ricci solitons and we provide some characterizations of rigidity, generalizing some known results for Ricci solitons. In the compact case we are able to deal with not…
This paper studies the polynomial stabilization of an elastic plate with dynamical boundary conditions on a non-smooth domain. To deal with the possible loss of solution regularity induced by boundary singularities, we formulate the problem…
We are concerned with the problem of determining the nonlinear term in a semilinear elliptic equation by boundary measurements. Precisely, we improve [5, Theorem 1.3], where a logarithmic type stability estimate was proved. We show actually…
A linear stability analysis of the hydrodynamic equations with respect to the homogeneous cooling state is carried out to identify the conditions for stability as functions of the wave vector, the dissipation, and the density. In contrast…
This work deals with Lipschitz stability for a parametric version of the general second order Ordinary Differential Equation (ODE) initial-value Cauchy problem. We first establish a Lipschitz stability result for this problem under a…
For a supersonic Euler flow past a straight wedge whose vertex angle is less than the extreme angle, there exists a shock-front emanating from the wedge vertex, and the shock-front is usually strong especially when the vertex angle of the…
Roll solutions at the zigzag boundary, typically selected by patterns and defects in numerical simulations, are shown to be nonlinearly stable. This result also serves as an example that linear decay weaker than the classical diffusive…
It is proved that, in two dimensions, the Calder\'on inverse conductivity problem in Lipschitz domains is stable in the $L^p$ sense when the conductivities are uniformly bounded in any fractional Sobolev space $W^{\alpha,p}$ $\alpha>0,…
We consider the inverse problem of determining the Lam\'e moduli for a piecewise constant elasticity tensor ${\mathbb C}= \sum_{j} {\mathbb C}_j \chi_{D_j}$, where $\{D_j\}$ is a known finite partition of the body $\Omega$, from the…
The study of provable adversarial robustness has mostly been limited to classification tasks and models with one-dimensional real-valued outputs. We extend the scope of certifiable robustness to problems with more general and structured…
In this Letter, we present a rigorous method to study the stability of periodic lasing systems. In a linear model, the presence of a continuum of modes (with arbitrarily close lasing thresholds) gives the impression that stable single-mode…