Palencia José Luis Díaz, Otero Abraham
Department of Information Technology, Escuela Politecnica Superior, Universidad San Pablo-CEU, CEU Universities, Campus Monteprincipe, Boadilla del Monte, Madrid 28668, Spain.
Department of Mathematics and Didactics, Universidad a Distancia de Madrid, UDIMA, Madrid, Spain.
Math Biosci Eng. 2023 Jun 8;20(7):13200-13221. doi: 10.3934/mbe.2023589.
The main goal of the presented study is to introduce a model of a pairwise invasion interaction with a nonlinear diffusion and advection. The new equation is based on the further general works introduced by Bramson (1988) to describe the invasive-invaded dynamics. This type of model is made particular with a density dependent diffusion along with an advection term. The new resulting model is then analyzed to explore the regularity, existence and uniqueness of solutions. It is well known that density dependent diffusion operators induce a propagating front with finite speed for compactly supported functions. Based on this, we introduce an analytical approach to determine the evolution of such a propagating front in the invasion dynamics. Afterward, we study the problem with travelling wave profiles and a numerical assessment. As a main finding to remark: When both species propagate with significantly different travelling wave speeds, the interaction becomes unstable, while when the species propagate with similar low speeds, the interaction stabilizes.
本研究的主要目标是引入一个具有非线性扩散和对流的成对入侵相互作用模型。新方程基于布拉姆森（1988年）提出的进一步的一般性工作，以描述入侵 - 被入侵动态。这种类型的模型通过密度依赖扩散以及对流项而变得特殊。然后对新得到的模型进行分析，以探索解的正则性、存在性和唯一性。众所周知，密度依赖扩散算子会为紧支集函数诱导出具有有限速度的传播前沿。基于此，我们引入一种解析方法来确定入侵动态中这种传播前沿的演化。之后，我们研究行波剖面问题并进行数值评估。作为一个主要发现值得注意的是：当两个物种以显著不同的行波速度传播时，相互作用变得不稳定，而当物种以相似的低速传播时，相互作用则稳定下来。
