Related papers: In search of Robbins stability
We present a stability result for a wide class doubly nonlinear equations, featuring general maximal monotone operators, and (possibly) nonconvex and nonsmooth energy functionals. The limit analysis resides on the reformulation of the…
We consider a system of random autonomous ODEs introduced by Cugliandolo et al. [22], which serves as a non-relaxational analog of the gradient flow for the spherical p-spin model. The asymptotics for the expected number of equilibria in…
This thesis studies qualitative properties of solutions to nonlinear elliptic equations of Poisson type with Dirichlet boundary conditions that arise from some physical phenomena, with a particular focus on regularity, stability, and…
The stability of stationary solutions of first-order systems of PDE's are considered. They may include some singular geometric terms, leading to discontinuous flux and non-conservative products. Based on several examples in Fluid Mechanics,…
We report a rigorous theory to show the origin of the unexpected periodic behavior seen in the consecutive differences between prime numbers. We also check numerically our findings to ensure that they hold for finite sequences of primes,…
Turbulent suspensions of heavy particles in incompressible flows have gained much attention in recent years. A large amount of work focused on the impact that the inertia and the dissipative dynamics of the particles have on their dynamical…
Nature is intrinsically heterogeneous, and remarkable phenomena can only be observed in the presence of intrinsically nonlinear heterogeneities. Spontaneous pattern formation in nature has fascinated humankind for centuries, and the…
The stability properties and perturbation-induced dynamics of the full set of stationary states of the nonlinear Schroedinger equation are investigated numerically in two physical contexts: periodic solutions on a ring and confinement by a…
By analyzing two Kinetically Constrained Models of supercooled liquids we show that the anomalous transport of a driven tracer observed in supercooled liquids is another facet of the phenomenon of dynamical heterogeneity. We focus on the…
We investigate the dynamics of $N$ point vortices in the plane, in the limit of large $N$. We consider {\em relative equilibria}, which are rigidly rotating lattice-like configurations of vortices. These configurations were observed in…
We derive a sufficient condition for stability in probability of an equilibrium of a randomly perturbed map in ${\mathbb R}^d$. This condition can be used to stabilize weakly unstable equilibria by random forcing. Analytical results on…
In this paper, we address the problem of robust stability for uncertain sampled-data systems controlled by a discrete-time disturbance observer (DT-DOB). Unlike most of previous works that rely on the small-gain theorem, our approach is to…
The widely claimed replicability crisis in science may lead to revised standards of significance. The customary frequentist confidence intervals, calibrated through hypothetical repetitions of the experiment that is supposed to have…
In this paper, We study an one--dimensional morphogenesis model considered by C. Stinner et al. in (Math. Meth. Appl. Sci. 2012,35 (445-465). Under homogeneous boundary conditions, we prove the existence of nonconstant positive steady…
The spatiotemporal complexity induced by perturbed initial excitations through the development of modulational instability in nonlinear lattices with or without disorder, may lead to the formation of very high amplitude, localized transient…
The well-posedness and regularity properties of diffusion-aggregation equations, emerging from interacting particle systems, are established on the whole space for bounded interaction force kernels by utilizing a compactness convergence…
In this paper, we consider the Stokes equations and we are concerned with the inverse problem of identifying a Robin coefficient on some non accessible part of the boundary from available data on the other part of the boundary. We first…
In this paper, we investigate the stabilizers of certain multisets $\mod p^k$ with respect to their natural multiplicative action, completely describing them for a certain family of polynomials whenever $p$ is an odd prime. This elucidates…
We investigate the stability with respect to homogenization of classes of integrals arising in the control-theoretic interpretation of some Hamilton-Jacobi equations. The prototypical case is the homogenization of energies with a Lagrangian…
We investigate stability of both localized time-periodic coherent states (pulsons) and uniformly distributed coherent states (oscillating condensate) of a real scalar field satisfying the Klein-Gordon equation with a logarithmic…