Clarissa Astuto, Jan Haskovec, Peter Markowich, Simone Portaro
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引用次数: 0
Abstract
We study self-regulating processes modeling biological transportation networks as presented in [15]. In particular, we focus on the 1D setting for Dirichlet and Neumann boundary conditions. We prove an existence and uniqueness result under the assumption of positivity of the diffusivity $ D $. We explore systematically various scenarios and gain insights into the behavior of $ D $ and its impact on the studied system. This involves analyzing the system with a signed measure distribution of sources and sinks. Finally, we perform several numerical tests in which the solution $ D $ touches zero, confirming the previous hints of local existence in particular cases.
我们研究了模拟生物运输网络的自调节过程,如[15]所示。我们特别关注Dirichlet和Neumann边界条件的一维设置。我们证明了在扩散系数为正的假设下的一个存在唯一性结果。我们系统地探索各种场景,并深入了解$ D $的行为及其对所研究系统的影响。这包括用源和汇的有符号测量分布来分析系统。最后,我们进行了几个解$ D $为零的数值测试,在特定情况下证实了前面的局部存在性提示。
期刊介绍:
The Journal of Dynamics and Games (JDG) is a pure and applied mathematical journal that publishes high quality peer-review and expository papers in all research areas of expertise of its editors. The main focus of JDG is in the interface of Dynamical Systems and Game Theory.