Local and Global Existence for Nonlocal Multispecies Advection-Diffusion Models
Local and Global Existence for Nonlocal Multispecies Advection-Diffusion Models
复制标题
DOI：
10.1137/21m1425992
复制
发表时间：
2022-01-01
影响因子：
2.1
通讯作者：
Potts, Jonathan R.
中科院分区：
文献类型：
--
作者：
Giunta, Valeria;Hillen, Thomas;Potts, Jonathan R.
非局部平流是一系列生物系统中的关键过程，从个体内的细胞到整个生物体的运动。因此，近年来，非局部平流的数学建模受到越来越多的关注。这些通常采取偏微分方程的形式，积分项模拟非局部性。一个常见的形式是聚集扩散方程，一类具有非局部对流的对流扩散模型。这最初是用来模拟一个单一的人口，但最近已扩展到多物种的情况下，生物体可能会改变其运动的共存物种的存在下建模。在这里，我们证明了一类非局部多种群对流扩散模型的存在性定理，具有任意数量的共存物种。我们证明了n = 1维空间模型的整体存在性和n > 1维空间模型的局部存在性。我们描述了一个有效的谱方法数值求解这些模型，并提供了一个例子模拟输出。总的来说，这有助于为研究物种间相互作用对运动和空间利用的影响提供坚实的数学基础。
Nonlocal advection is a key process in a range of biological systems, from cells within individuals to the movement of whole organisms. Consequently, in recent years, there has been increasing attention on modeling non-local advection mathematically. These often take the form of partial differential equations, with integral terms modeling the nonlocality. One common formalism is the aggregation-diffusion equation, a class of advection-diffusion models with nonlocal advection. This was originally used to model a single population but has recently been extended to the multispecies case to model the way organisms may alter their movement in the presence of coexistent species. Here we prove existence theorems for a class of nonlocal multispecies advection-diffusion models, with an arbitrary number of coexistent species. We prove global existence for models in n = 1 spatial dimension and local existence for n > 1. We describe an efficient spectral method for numerically solving these models and provide an example simulation output. Overall, this helps provide a solid mathematical foundation for studying the effect of interspecies interactions on movement and space use.