论文标题
野外扩散模型：基本解决方案和渐近行为
The field-road diffusion model: fundamental solution and asymptotic behavior
论文作者
论文摘要
我们考虑线性野外道路系统，这是人口动态和生态学中快速扩散通道的模型。该系统采用在不同维度和交换边界条件的域上设置的PDE系统的形式。尽管问题的几何形状具有复杂的几何形状，但我们为其基本解决方案和解决相关库奇问题的解决方案提供了明确的表达。主要工具是傅立叶（在道路变量上）/拉普拉斯（按时）变换。此外，我们得出了这些解决方案的$ l^{\ infty} $规范的衰减率的估计。
We consider the linear field-road system, a model for fast diffusion channels in population dynamics and ecology. This system takes the form of a system of PDEs set on domains of different dimensions, with exchange boundary conditions. Despite the intricate geometry of the problem, we provide an explicit expression for its fundamental solution and for the solution to the associated Cauchy problem. The main tool is a Fourier (on the road variable)/Laplace (on time) transform. In addition, we derive estimates for the decay rate of the $L^{\infty}$ norm of these solutions.
