论文标题
非线性迁移率的聚集扩散方程的确定粒子近似
Deterministic particle approximation of aggregation diffusion equations with nonlinear mobility
论文作者
论文摘要
我们考虑具有Lipschitz非启动迁移率函数的无限型一维域上的一类聚合扩散方程。对于任何有限的初始数据的有限初始数据，我们显示了适当的确定性粒子近似与类聚合 - 扩散PDE的弱解（与经典的弱解决方案（与经典的弱解相吻合），我们显示出强的$ l^1 $ convergence。为了证明没有BV或无真空假设的方案的适当性和收敛性，并通过迁移率的存在来克服在这种情况下提出的问题，我们可以改善和加强ARXIV中引入的技术：2012.01966（2）。
We consider a class of aggregation-diffusion equations on unbounded one dimensional domains with Lipschitz nonincreasing mobility function. We show strong $L^1$-convergence of a suitable deterministic particle approximation to weak solutions of a class aggregation-diffusion PDEs (coinciding with the classical ones in the no vacuum regions) for any bounded initial data of finite energy. In order to prove well-posedness and convergence of the scheme with no BV or no vacuum assumptions and overcome the issues posed in this setting by the presence of a mobility function, we improve and strengthen the techniques introduced in arXiv:2012.01966(2).
