相关论文: An Infinite-Time Relaxation Theorem for Differenti…

The classical Hahn-Banach theorem is based on a successive point-by-point procedure of extending bounded linear functionals. In the setting of a general metric domain, the conditions are less restrictive and the extension is only required…

On the basis of physical considerations we propose a one-dimensional discrete lattice model for the density relaxation of granular materials under tapping. Solving the difference equation numerically, we find a logarithmic time-dependence…

A fully discrete approximation of the one-dimensional stochastic heat equation driven by multiplicative space-time white noise is presented. The standard finite difference approximation is used in space and a stochastic exponential method…

This paper develops a geometric framework for the stability analysis of differential inclusions governed by maximally monotone operators. A key structural decomposition expresses the operator as the sum of a convexified limit mapping and a…

In this note we investigate three kinds of applications of the Painlev\'e-Kuratowski convergence of closed sets in analysis that are motivated also by questions from singularity theory. Firstly, we generalise to Lipschitz functions the…

We investigate the late-time asymptotic behavior of solutions to nonlinear hyperbolic systems of conservation laws containing stiff relaxation terms. First, we introduce a Chapman-Enskog-type asymptotic expansion and derive an effective…

Integro-differential sweeping processes with prox-regular sets in Hilbert spaces have been the subject of various recent studies. Diverse applications of such differential inclusions to complementarity problems, electrical circuits,…

In this paper, under a one-sided Lipschitz condition on the drift coefficient we adopt (via contraction principle) a exponential approximation argument to investigate large deviations for neutral stochastic functional differential…

We present an alternative proof for the existence of solutions of stochastic functional differential equations satisfying a global Lipschitz condition. The proof is based on an approximation scheme in which the continuous path dependence…

In this note, we show a classical result on the local existence and uniqueness of a solution to an initial value problem subject to a Lipschitz condition. We use only elementary tools from mathematical analysis, without involving any…

We prove two rigidity theorems for maps between Riemannian manifolds. First, we prove that a Lipschitz map $f:M\to N$ between two oriented Riemannian manifolds, whose differential is almost everywhere an orientation-preserving isometry, is…

In this work, we describe how to approximate solutions of some partial differential equations using the finite difference method defined on the Minkowski self-similar curve.

We consider a modification of the so-called phase-field crystal (PFC) equation introduced by K.R. Elder et al. This variant has recently been proposed by P. Stefanovic et al. to distinguish between elastic relaxation and diffusion time…

This paper proves comparison principles for elliptic PDE involving the Finsler infinity Laplacian, a second-order differential operator with discontinuities in the gradient variable arising in $L^{\infty}$-variational problems and…

We carry out overdamped simulations in a simple model of jamming - a collection of bi-disperse soft core frictionless disks in two dimensions - with the aim to explore the finite size dependence of different quantities, both the relaxation…

For a well-posed non-selfadjoint indefinite second-order linear elliptic PDE with general coefficients $\mathbf A, \mathbf b,\gamma$ in $L^\infty$ and symmetric and uniformly positive definite coefficient matrix $\mathbf A$, this paper…

For a slow-fast system of the form $\dot{p}=\epsilon f(p,z,\epsilon)+h(p,z,\epsilon)$, $\dot{z}=g(p,z,\epsilon)$ for $(p,z)\in \mathbb R^n\times \mathbb R^m$, we consider the scenario that the system has invariant sets $M_i=\{(p,z):…

We prove existence and uniqueness of solutions to a class of stochastic semilinear evolution equations with a monotone nonlinear drift term and multiplicative noise, considerably extending corresponding results obtained in previous work of…

In this paper we consider the minimization of a novel class of fractional linear growth functionals involving the Riesz fractional gradient. These functionals lack the coercivity properties in the fractional Sobolev spaces needed to apply…

The aim of this tutorial survey is to revisit the basic theory of relaxation processes governed by linear differential equations of fractional order. The fractional derivatives are intended both in the Rieamann-Liouville sense and in the…