标题： 紧致度量图上的基态选择 显示英文标题

标题： Selection of the ground state on a compact metric graph

摘要： 我们证明了在边界顶点上具有狄利克雷条件的紧致度量图上的Fisher--KPP模型的基态要么是平凡的（零），要么是非平凡的且严格正的。 对于正初始数据，我们证明如果度量图的边是均匀小的，那么平凡基态是全局渐近稳定的；如果边是均匀大的，则非平凡基态是全局渐近稳定的。 对于中间情况，我们找到了平凡基态与非平凡基态存在性、唯一性和全局渐近稳定性的精确准则。 除了基于比较理论、能量极小值和图拉普拉斯矩阵最低特征值的标准方法外，我们还开发了一种基于微分方程周期函数的新方法，以表征花形图中的非平凡基态。 显示英文摘要

摘要： We show that the ground state in the Fisher--KPP model on a compact metric graph with Dirichlet conditions on boundary vertices is either trivial (zero) or nontrivial and strictly positive. For positive initial data, we prove that the trivial ground state is globally asymptotically stable if the edges of the metric graph are uniformly small and the nontrivial ground state is globally asymptotically stable if the edges are uniformly large. For the intermediate case, we find a sharp criterion for the existence, uniqueness and global asymptotic stability of the trivial versus nontrivial ground state. Besides standard methods based on the comparison theory, energy minimizers, and the lowest eigenvalue of the graph Laplacian, we develop a novel method based on the period function for differential equations to characterize the nontrivial ground state in the particular case of flower graphs.