Related papers: Dimension estimates for nonlinear nonautonomous sy…
A non-autonomous evolution semi-linear differential system under non-instantaneous impulses, delays, and perturbed by non-local conditions is studied. Its piece-wise continuous solutions belong to a finite-dimensional Banach space. The…
In this paper, we overview the recent progresses on the lifespan estimates of classical solutions of the initial value problems for nonlinear wave equations in one space dimension. There are mainly two directions of the developments on the…
We give a partial review of what is known so far on stability of periodically driven quantum systems versus regularity of the bounded driven force. In particular we emphasize the fact that unbounded degeneracies of the unperturbed…
We consider a differential system of neutral type with distributed delay. We obtain a precise norm estimation of solutions of the system in question on some nonclosed set. Our result is based on a spectral analysis of the operator and Riesz…
We establish Schauder-type estimates for linear parabolic systems driven by variable-coefficient nonlocal pseudo-differential operators of order $s>0$. These estimates are formulated in critical time-weighted H\"older/Besov-type spaces and…
We obtain large and moderate deviation estimates, as well as concentration inequalities, for a class of nonuniformly expanding maps with stretched exponential decay of correlations. In the large deviation regime, we also exhibit examples…
We discuss the analysis and stability of a family of cross-diffusion boundary value problems with nonlinear diffusion and drift terms. We assume that these systems are close, in a suitable sense, to a set of decoupled and linear problems.…
We establish some quantitative concentration estimates for the empirical measure of many independent variables, in transportation distances. As an application, we provide some error bounds for particle simulations in a model mean field…
First order optimization algorithms play a major role in large scale machine learning. A new class of methods, called adaptive algorithms, were recently introduced to adjust iteratively the learning rate for each coordinate. Despite great…
We study the dynamics of a non-minimally coupled scalar field cosmology with a potential function. We use the framework of dynamical systems theory to investigate all evolutional paths admissible for all initial conditions. Additionally, we…
We present a self-contained analysis of a particular family of metrics over the set of non-negative integers. We show that these metrics, which are defined through a nested sequence of optimal transport problems, provide tight estimates for…
In this article, we present an extension of the formulation recently developed by the authors (A Framework for Data-Driven Computational Mechanics Based on Nonlinear Optimization, arXiv:1910.12736 [math.NA]) to the structural dynamics…
We develop a framework to give upper bounds on the "practical" computational complexity of stability problems for a wide range of nonlinear continuous and hybrid systems. To do so, we describe stability properties of dynamical systems using…
We derive optimal estimates for the Bergman kernel and the Bergman metric for certain model domains in $\mathbb{C}^2$ near boundary points that are of infinite type. Being unbounded models, these domains obey certain geometric constraints…
Local nonlinear approximations to the growth of cosmic perturbations are developed, resulting in relations, at a given epoch, between the peculiar velocity and gravity fields and their gradients. Only the equation of motion is approximated,…
We provide a general approach to Lipschitz regularity of solutions for a large class of vector-valued, nonautonomous variational problems exhibiting nonuniform ellipticity. The functionals considered here range amongst those with unbalanced…
Non-autonomous iterated function systems are a generalization of iterated function systems. If the contractions in the system are conformal mappings, it is called a non-autonomous conformal iterated function system, and its attractor is…
We provide explicit conditions for uniform stability, global asymptotic stability and uniform exponential stability for dynamic equations with a single delay and a nonnegative coefficient. Some examples on nonstandard time scales are also…
We present some results in the analysis of non-compact differential equations on unbounded domains.
In this paper, we present a new approach to obtain so-called damping estimates for self-similar solutions to general hyperbolic relaxation systems applying the method of characteristics. Such damping estimates are an important part of the…