This article is cited in 3 scientific papers (total in 3 papers)
Asymptotics of parabolic Green's functions on lattices
a Free University of Berlin, Germany
b Peoples' Friendship University, Russia
For parabolic spatially discrete equations, we consider Green's functions, also known as heat kernels on lattices. We obtain their asymptotic expansions with respect to powers of time variable $t$ up to an arbitrary order and estimate the remainders uniformly on the entire lattice. The spatially discrete (difference) operators under consideration are finite-difference approximations of continuous strongly elliptic differential operators (with constant coefficients) of arbitrary even order in $\mathbb R^d$ with arbitrary $d\in\mathbb N$. This genericity, besides numerical and deterministic lattice-dynamics applications, allows one to obtain higher-order asymptotics of transition probability functions for continuous-time random walks on $\mathbb Z^d$ and other lattices.
spatially discrete parabolic equations, asymptotics, discrete Green functions, lattice Green functions, heat kernels of lattices, continuous-time random walks.
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St. Petersburg Mathematical Journal, 2017, 28:5, 569–596
P. Gurevich, “Asymptotics of parabolic Green's functions on lattices”, Algebra i Analiz, 28:5 (2016), 21–60; St. Petersburg Math. J., 28:5 (2017), 569–596
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\paper Asymptotics of parabolic Green's functions on lattices
\jour Algebra i Analiz
\jour St. Petersburg Math. J.
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P. Gurevich, S. Tikhomirov, “Rattling in spatially discrete diffusion equations with hysteresis”, Multiscale Model. Simul., 15:3 (2017), 1176–1197
P. Gurevich, S. Tikhomirov, “Spatially discrete reaction-diffusion equations with discontinuous hysteresis”, Ann. Inst. Henri Poincare-Anal. Non Lineaire, 35:4 (2018), 1041–1077
Gurevich P., “Asymptotics of the Heat Kernels on 2D Lattices”, Asymptotic Anal., 112:1-2 (2019), 107–124
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