This paper studies a dissipative heat equation with Delta sources of non-linear strength located on a periodic lattice. The model arises from intracellular waves in continuum excitable media with discrete release sites. Due to the presence of Delta sources, the solution of the model has discontinuous spatial derivatives. We focus on the bistable regime of the model, determined by the decay strength parameter a and the separation distance L between release sites, in which the model admits exactly three L-periodic steady states. We establish the existence of pulsating waves spatially connecting them. For the case of waves connecting two stable L-periodic steady states, the uniqueness and global exponential stability of pulsating waves are shown. Also a new technique is introduced to find the fine structure of the tails of pulsating waves.

本文研究了位于周期性晶格上的非线性强度的Delta源的耗散热方程。该模型源自具有离散释放位点的连续可激发介质中的细胞内波。由于存在Delta来源，因此模型的解具有不连续的空间导数。我们专注于模型的双稳态状态，该状态由衰减强度参数a和释放位置之间的间隔距离L决定，在该状态下，模型恰好允许三个L周期稳态。我们建立了在空间上将它们连接起来的脉动波的存在。对于波浪连接两个稳定L的情况-周期稳态，显示了脉动波的唯一性和整体指数稳定性。还引入了一种新技术来寻找脉动波尾部的精细结构。