论文标题
具有对数灵敏度和逻辑生长的趋化性PDE模型
A PDE model for chemotaxis with logarithmic sensitivity and logistic growth
论文作者
论文摘要
在本文中，我们研究了具有对数灵敏度和逻辑生长的排斥趋化模型的初始有限值问题及其渐近行为。我们为具有Neumann边界条件的大型初始数据建立了强大解决方案的全球良好性，并确定了定性结果，即种群密度和化学浓度均非人口密度专门融合到其承载能力的恒定状态。我们还证明，在该方案中，化学扩散率极限存在。最后，我们提供了严格的定性结果的数值确认，以及证明量表现象分离的数值模拟。
In this paper, we study the initial-boundary value problem and its asymptotic behavior for a repulsive chemotaxis model with logarithmic sensitivity and logistic growth. We establish global well-posedness of strong solutions for large initial data with Neumann boundary conditions and, moreover, establish the qualitative result that both the population density and chemical concentration asymptotically converge to constant states with the population density specifically converging to its carrying capacity. We additionally prove that the vanishing chemical diffusivity limit holds in this regime. Lastly, we provide numerical confirmation of the rigorous qualitative results, as well as numerical simulations that demonstrate a separation of scales phenomenon.
