二维格上热核的渐近性
Asymptotics of the heat kernels on 2D lattices
摘要：
我们获得了空间离散的二维热核或格上的格林函数关于时间变量的幂的渐近展开，直到任意阶，并在整个格上一致地估计了幂。与一维情形不同，渐近性包含一个与时间无关的项。其空间渐近性的推导是本文的技术核心。除了数值应用外，所得结果在分析格点上反应扩散方程的时空模式，特别是滞回扩散系统的摇铃模式中起着至关重要的作用。
英文摘要：
We obtain asymptotic expansions of the spatially discrete 2D heat kernels, or Green's functions on lattices, with respect to powers of time variable up to an arbitrary order and estimate the remainders uniformly on the whole lattice. Unlike in the 1D case, the asymptotics contains a time independent term. The derivation of its spatial asymptotics is the technical core of the paper. Besides numerical applications, the obtained results play a crucial role in the analysis of spatio-temporal patterns for reaction-diffusion equations on lattices, in particular rattling patterns for hysteretic diffusion systems.
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