论文标题
局部/非局部扩散模型
A local/nonlocal diffusion model
论文作者
论文摘要
在本文中，我们研究了一些定性特性，用于将作用于两个不同子域作用的局部和非局部扩散算子结合在一起，并以这样的方式耦合，因此所产生的进化问题是能量功能的梯度流。耦合发生在发生不同扩散的区域之间的接口上。我们证明存在和唯一性结果以及该模型保留了初始条件的总质量。我们还研究了解决方案的渐近行为。最后，我们展示了一种合适的方法，可以从非局部重新固定内核处恢复整个域的热量方程。
In this paper, we study some qualitative properties for an evolution problem that combines local and nonlocal diffusion operators acting in two different subdomains and, coupled in such a way that, the resulting evolution problem is the gradient flow of an energy functional. The coupling takes place at the interface between the regions in which the different diffusions take place. We prove existence and uniqueness results, as well as, that the model preserves the total mass of the initial condition. We also study the asymptotic behavior of the solutions. Finally, we show a suitable way to recover the heat equation at the whole domain from taking the limit at the nonlocal rescaled kernel.
