Error estimate for the Finite Volume Scheme applied to the advection equation

带粗糙系数的对流扩散方程有限体积格式的误差估计

Error estimates for a finite volume scheme for advection-diffusion equations with rough coefficients

该研究针对低正则性DiPerna-Lions框架下带粗糙系数的对流扩散方程，分析隐式迎风有限体积格式的收敛性，证明非结构正则网格上收敛速率至少为一阶，并通过对数Kantorovich-Rubinstein距离给出弱收敛误差界。

应用于稳态平流方程的带 Neumann 边界条件的椭圆正则化的强收敛性

On strong convergence of an elliptic regularization with the Neumann boundary condition applied to a stationary advection equation

本文研究稳态平流方程在 Neumann 边界条件下椭圆正则化的强收敛性，证明了解的 $L^2$ 强收敛并给出依赖于解正则性和边界与平流场关系的收敛速率，数值实验验证了估计的最优性。

A reaction-diffusion-advection equation with mixed and free boundary conditions

We investigate a reaction-diffusion-advection equation of the form $u_t-u_{xx}+βu_x=f(u)$ $(t>0,\,0<x<h(t))$ with mixed boundary condition at $x=0$ and a free boundary condition at $x=h(t)$. Such a model may be applied to describe the dynamical process of a new or invasive species adopting a combination of random movement and advection upward or downward along the resource gradient, with the free boundary representing the expanding front. The goal of this paper is to understand the effect of advection environment and no flux across the left boundary on the dynamics of this species. When $|β|<c…

关于准线性模式形成反应-扩散-对流系统的吉因斯-兰道近似

On the Ginzburg-Landau approximation for quasilinear pattern forming reaction-diffusion-advection systems

本文证明吉因斯-兰道方程能准确预测准线性模式形成反应-扩散-对流系统的动力学，并应用于格雷-斯科特-克劳斯梅尔模型。

用于非线性一维抛物型偏微分方程的IMEX-RK有限体积法及其在期权定价中的应用

IMEX-RK finite volume methods for nonlinear 1d parabolic PDEs. Application to option pricing

本文提出二阶IMEX-RK有限体积格式求解期权定价中的一维非线性抛物型偏微分方程，对流项显式、扩散项隐式处理，兼具计算高效、二阶精度及可扩展至高阶的优势。

Dirichlet边界条件下的一维种群动力学中的粘附与体积填充

Adhesion and volume filling in one-dimensional population dynamics under Dirichlet boundary condition

本文推广了一维细胞粘附与体积填充种群模型，将其方程分为六类，并针对其中一类前向-后向-前向型对流扩散方程，利用凸积分方法证明了当初始密度最大值超过阈值时Dirichlet边值问题存在无穷多个全局弱解，这些解先经历细尺度混合后光滑化并指数衰减到零。