Wavefronts for degenerate diffusion-convection reaction equations with sign-changing diffusivity

含累积项和聚集运动的反应-扩散-对流模型的波前解

Wavefront Solutions for Reaction-diffusion-convection Models with Accumulation Term and Aggregative Movements

本文分析含累积项和聚集运动的单稳型反应-扩散-对流模型波前解，允许扩散系数与累积项有限符号变化，给出行波解存在性与阈值波速估计，并将其分为经典型和尖锐型。

Global well-posedness for a rapidly rotating convection model of tall columnar structure in the limit of infinite Prandtl number

We analyze a three-dimensional rapidly rotating convection model of tall columnar structure in the limit of infinite Prandtl number, i.e., when the momentum diffusivity is much more dominant than the thermal diffusivity. Consequently, the dynamics of the velocity field takes place at a much faster time scale than the temperature fluctuation, and at the limit the velocity field formally adjusts instantaneously to the thermal fluctuation. We prove the global well-posedness of weak solutions and strong solutions to this model.

Initial-boundary value problem to 2D Boussinesq equations for MHD convection with stratification effects

This paper is concerned with the initial-boundary value problem to 2D magnetohydrodynamics-Boussinesq system with the temperature-dependent viscosity, thermal diffusivity and electrical conductivity. First, we establish the global weak solutions under the minimal initial assumption. Then by imposing higher regularity assumption on the initial data, we obtain the global strong solution with uniqueness. Moreover, the exponential decay estimate of the solution is obtained.

Sharp profiles in models of collective movements

We consider a parabolic partial differential equation that can be understood as a simple model for crowds flows. Our main assumption is that the diffusivity and the source/sink term vanish at the same point; the nonhomogeneous term is different from zero at any other point and so the equation is not monostable. We investigate the existence, regularity and monotone properties of semi-wavefront solutions as well as their convergence to wavefront solutions.

无热扩散的三维快速旋转对流模型分析

Analysis of a three-dimensional rapidly rotating convection model without thermal diffusion

本文针对无热扩散的三维快速旋转对流模型，通过先研究带热扩散的正则化模型并建立与扩散系数无关的精细估计，证明了弱解的全局存在唯一性和强解的Hadamard适定性。

具有退化扩散性的反应-扩散系统的波前及其在细菌生长模型中的应用

Wavefronts for a degenerate reaction-diffusion system with application to bacterial growth models

针对Kawasaki等人提出的细菌生长反应-扩散模型波前解缺乏解析证明的问题，研究者利用打靶法、Fréchet空间不动点理论和中心流形定理，证明了无穷多族由波速参数化的波前存在，并给出阈值速度的上下界。

Convergence of stochastic structure-preserving schemes for computing effective diffusivity in random flows

In this paper, we propose stochastic structure-preserving schemes to compute the effective diffusivity for particles moving in random flows. We first introduce the motion of particles using the Lagrangian formulation, which is modeled by stochastic differential equations (SDEs). We also discuss the definition of the corrector problem and effective diffusivity. Then we propose stochastic structure-preserving schemes to solve the SDEs and provide a sharp convergence analysis for the numerical schemes in computing effective diffusivity. The convergence analysis follows a probabilistic approach, w…