Related papers: Convergence results for a coarsening model using g…
In this paper, we aim to study the motions of interfaces and coarsening rates governed by the time-fractional Cahn--Hilliard equation (TFCHE). It is observed by many numerical experiments that the microstructure evolution described by the…
A network of locally interacting agents can be thought of as performing a distributed computation. But not all computations can be faithfully distributed. This paper investigates which global, linear transformations can be computed using…
This article is devoted to the analysis of the weak rates of convergence of schemes introduced by the authors in a recent work, for the temporal discretization of the stochastic Allen-Cahn equation driven by space-time white noise. The…
In this paper we propose an explicit fully discrete scheme to numerically solve the stochastic Allen-Cahn equation. The spatial discretization is done by a spectral Galerkin method, followed by the temporal discretization by a tamed…
This paper is concerned with the sharp interface limit for the Allen-Cahn equation with a nonlinear Robin boundary condition in a bounded smooth domain $\Omega\subset\mathbb{R}^2$. We assume that a diffuse interface already has developed…
We prove global well-posedness for the defocusing cubic wave equation with data in $H^{s} \times H^{s-1}$, $1>s>{13/18}$. The main task is to estimate the variation of an almost conserved quantity on an arbitrary long time interval. We…
A characterization of the general linear equation in standard form admitting a maximal symmetry algebra is obtained in terms of a simple set of conditions relating the coefficients of the equation. As a consequence, it is shown that in its…
We introduce a modified Consensus-Based Optimization model that admits a fully unified and rigorous analysis of its finite-particle dynamics, the associated McKean--Vlasov equation, and their optimization behavior under a single set of…
The violent relaxation and the metastable states of the Hamiltonian Mean-Field model, a paradigmatic system of long-range interactions, is studied using a Hamiltonian formalism. Rigorous results are derived algebraically for the time…
In applications, a substantial number of problems can be formulated as non-linear least squares problems over smooth varieties. Unlike the usual least squares problem over a Euclidean space, the non-linear least squares problem over a…
A mathematical model for the discrete nonlinear fragmentation (collision-induced breakage) equation with diffusion is studied. The existence of global weak solutions is established in arbitrary spatial dimensions without assuming a strictly…
Although applications of Bayesian analysis for numerical quadrature problems have been considered before, it's only very recently that statisticians have focused on the connections between statistics and numerical analysis of differential…
We address the numerical discretization of the Allen-Cahn prob- lem with additive white noise in one-dimensional space. The discretization is conducted in two stages: (1) regularize the white noise and study the regularized problem, (2)…
In this paper we construct space-time full discretizations of stochastic Allen-Cahn equations driven by space-time white noise on 2D torus. The approximations are implemented by tamed exponential Euler discretization in time and spectral…
In this paper we propose a solution strategy for the Cahn-Larch\'e equations, which is a model for linearized elasticity in a medium with two elastic phases that evolve subject to a Ginzburg-Landau type energy functional. The system can be…
This paper examines an averaging technique applied to the transport equations as an alternative to vanishing viscosity. Such techniques have been shown to be valid shock-regularizations of the Burgers equation and the Euler equations, but…
In this note, we provide an overarching analysis of primal-dual dynamics associated to linear equality-constrained optimization problems using contraction analysis. For the well-known standard version of the problem: we establish…
It was recently realized that the persistence exponent appearing in the dynamics of nonequilibrium systems is a special member of a continuously varying family of exponents, describing generalized persistence properties. We propose and…
In this paper, we investigate gradient estimate of the Poisson equation and the exponential convergence in the Wasserstein metric $W_{1,d_{l^1}}$, uniform in the number of particles, and uniform-in-time propagation of chaos for the…
Generalized impedance boundary conditions are effective, approximate boundary conditions that describe scattering of waves in situations where the wave interaction with the material involves multiple scales. In particular, this includes…