论文标题
聚合扩散方程的完全离散和消耗能量的有限体积方案的收敛
Convergence of a Fully Discrete and Energy-Dissipating Finite-Volume Scheme for Aggregation-Diffusion Equations
论文作者
论文摘要
我们研究了一种隐式有限体积方案，用于非线性非本地聚集 - 扩散方程，该方程表现出梯度流结构，该方程最近由Bailo，Carrillo和Hu（2020）引入。至关重要的是，该方案保持了相关的完全离散能量的耗散属性，并且在时间步骤方面无条件地做到这一点。我们在这项工作中的主要贡献是在适当的假设上表明该方法的收敛性在涉及的扩散函数和潜力上。
We study an implicit finite-volume scheme for non-linear, non-local aggregation-diffusion equations which exhibit a gradient-flow structure, recently introduced by Bailo, Carrillo, and Hu (2020). Crucially, this scheme keeps the dissipation property of an associated fully discrete energy, and does so unconditionally with respect to the time step. Our main contribution in this work is to show the convergence of the method under suitable assumptions on the diffusion functions and potentials involved.
