相关论文: Minimizing movements solutions for a monotone mode…

In many biological systems, motile agents exhibit random motion with short-term directional persistence, together with crowding effects arising from spatial exclusion. We formulate and study a class of lattice-based models for multiple…

We derive a simple criterion that ensures uniqueness, Lipschitz stability and global convergence of Newton's method for the finite dimensional zero-finding problem of a continuously differentiable, pointwise convex and monotonic function.…

This paper concerns periodic solutions for a 1D-model with nonlocal velocity given by the periodic Hilbert transform. There is a rich literature showing that this model presents singular behavior of solutions via numerics and mathematical…

We propose notions of minimax and viscosity solutions for a class of fully nonlinear path-dependent PDEs with nonlinear, monotone, and coercive operators on Hilbert space. Our main result is well-posedness (existence, uniqueness, and…

Uniqueness of the finite element solution for nonmonotone quasilinear problems of elliptic type is established in one and two dimensions. In each case, we prove a comparison theorem based on locally bounding the variation of the discrete…

We consider the problem of minimization of a convex function on a simple set with convex non-smooth inequality constraint and describe first-order methods to solve such problems in different situations: smooth or non-smooth objective…

We prove the existence of a weak global in time mean curvature flow of a bounded partition of space using the method of minimizing movements. The result is extended to the case when suitable driving forces are present. We also prove some…

A continuum individual-based model of hopping and coalescing particles is introduced and studied. Its microscopic dynamics are described by a hierarchy of evolution equations obtained in the paper. Then the passage from the micro- to…

We consider the maximal displacement of one dimensional branching Brownian motion with (macroscopically) time varying profiles. For monotone decreasing variances, we show that the correction from linear displacement is not logarithmic but…

This paper addresses the ill-posedness of the classical Rayleigh variational model of conducting charged liquid drops by incorporating the discreteness of the elementary charges. Introducing the model that describes two immiscible fluids…

This work introduces finite element methods for a class of elliptic fully nonlinear partial differential equations. They are based on a minimal residual principle that builds upon the Alexandrov--Bakelman--Pucci estimate. Under rather…

In an abstract Banach space we study conditions for the existence of piecewise continuous, almost periodic solutions for semi-linear impulsive differential equation with fixed and non-fixed moments of impulsive action

This paper investigates the nonlinear dynamics of Newton's problem of minimal resistance in radial fields. We move beyond classical translational symmetry to analyze two non-equilibrium scenarios: a scale-invariant free expansion and an…

We consider the $N$-body problem in $\mathbb{R}^d$ with the newtonian potential $1/r$. We prove that for every initial configuration $x_i$ and for every minimizing normalized central configuration $x_0$, there exists a collision-free…

We propose an adaptive finite element algorithm to approximate solutions of elliptic problems whose forcing data is locally defined and is approximated by regularization (or mollification). We show that the energy error decay is…

The aim of this paper is studying the problem of almost periodicity of almost periodic lattice dynamical systems of the form $u_{i}'=\nu (u_{i-1}-2u_i+u_{i+1})-\lambda u_{i}+F(u_i)+f_{i}(t)\ (i\in \mathbb Z,\ \lambda >0)$. We prove the…

We consider the problem of placing n small balls of given radius in a certain domain subject to a force f in order to minimize the compliance of the configuration. Then we let n tend to infinity and look at the asymptotics of the…

We consider a system of nonlinear partial differential equations describing the motion of an incompressible chemically reacting generalized Newtonian fluid in three space dimensions. The governing system consists of a steady…

Discontinuous dynamical systems with grazing solutions are discussed. The group property, continuation of solutions, continuity and smoothness of motions are thoroughly analyzed. A variational system around a grazing solution which depends…

In this paper we study the shape of least-energy solutions to a singularly perturbed quasilinear problem with homogeneous Neumann boundary condition. We use an intrinsic variation method to show that at limit, the global maximum point of…