Related papers: Sharp interface limit for stochastically perturbed…

In Becker and Jentzen (2019) and Becker et al. (2017), an explicit temporal semi-discretization scheme and a space-time full-discretization scheme were, respectively, introduced and analyzed for the additive noise-driven stochastic…

We investigate the Cahn-Hilliard and the conserved Allen-Cahn equations with logarithmic type potential and conservative noise in a periodic domain. These features ensure that the order parameter takes its values in the physical range and,…

White noise-driven nonlinear stochastic partial differential equations (SPDEs) of parabolic type are frequently used to model physical and biological systems in space dimensions d = 1,2,3. Whereas existence and uniqueness of weak solutions…

We establish the unique ergodicity of a fully discrete scheme for monotone SPDEs with polynomial growth drift and bounded diffusion coefficients driven by multiplicative white noise. The main ingredient of our method depends on the…

Motivated by practical applications in heat conduction and contaminant transport, we consider heat and mass diffusion across a perturbed interface separating two finite regions of distinct diffusivity. Under the assumption of continuity of…

We establish sharp estimates for the convergence rate of the Kranosel'ski\v{\i}-Mann fixed point iteration in general normed spaces, and we use them to show that the asymptotic regularity bound recently proved in [11] (Israel Journal of…

In this article, we study the behavior of the Abels-Garcke-Gr\"un Navier-Stokes-Cahn-Hilliard diffuse-interface model for binary-fluid flows, as the diffuse-interface thickness passes to zero. We consider this so-called sharp-interface…

Stochastic averaging problems with Gaussian forcing have been studied thoroughly for many years, but far less attention has been paid to problems where the stochastic forcing has infinite variance, such as an {\alpha}-stable noise forcing.…

For an arbitrary strong, spherically symmetric super-horizon curvature perturbation, we present analytical solutions of the Einstein equations in terms of asymptotic expansion over the ratio of the Hubble radius to the length-scale of the…

We study the roughening properties of the anharmonic elastic interface in the presence of temporally correlated noise. The model can be seen as a generalization of the anharmonic Larkin model, recently introduced by Purrello, Iguain, and…

We investigate the mass-preserving $L^2$-gradient flow associated with a generalized Cahn--Hilliard equation. Our focus is on the sharp interface regime, where the interface width parameter $\varepsilon > 0$ is small. For well-prepared…

We consider the sharp interface limit of the Allen-Cahn equation with Dirichlet or dynamic boundary conditions and give a varifold characterization of its limit which is formally a mean curvature flow with Dirichlet or dynamic boundary…

Stochastic approximation is a powerful class of algorithms with celebrated success. However, a large body of previous analysis focuses on stochastic approximations driven by contractive operators, which is not applicable in some important…

We study the stochastic mass-conserving Allen-Cahn equation posed on a bounded two-dimensional domain with additive spatially smooth space-time noise. This equation associated with a small positive parameter describes the stochastic motion…

We study the convergence of a Zakharov system driven by a time white noise, colored in space, to a multiplicative stochastic nonlinear Schr{\"o}dinger equation, as the ion-sound speed tends to infinity. In the absence of noise, the…

We present the microscopic equation of growing interface with quenched noise for the Tang and Leschhorn model [{\em Phys. Rev.} {\bf A 45}, R8309 (1992)]. The evolution equations for the mean heigth and the roughness are reached in a simple…

We study the long time statistics of a class of semi--linear damped wave equations with polynomial nonlinearities and perturbed by additive Gaussian noise in dimensions 2 and 3. We find that if sufficiently many directions in the phase…

We prove an asymptotic coupling theorem for the $2$-dimensional Allen--Cahn equation perturbed by a small space-time white noise. We show that with overwhelming probability two profiles that start close to the minimisers of the potential of…

In this paper, the compressible immiscible two-phase flow with relaxation is investigated, this model can be regarded as a natural modification of Jin-Xin relaxation scheme proposed and developed by S.Jin and Z.P.Xin([Comm.Pure Appl.Math.,…

In the study of geometric surface evolutions, stochastic reaction-diffusion equation provides a powerful tool for capturing and simulating complex dynamics. A critical challenge in this area is developing numerical approximations that…