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Algebra i Analiz, 2016, Volume 28, Issue 5, Pages 21–60 (Mi aa1506)  

This article is cited in 3 scientific papers (total in 3 papers)

Research Papers

Asymptotics of parabolic Green's functions on lattices

P. Gurevichab

a Free University of Berlin, Germany
b Peoples' Friendship University, Russia

Abstract: 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.

Keywords: spatially discrete parabolic equations, asymptotics, discrete Green functions, lattice Green functions, heat kernels of lattices, continuous-time random walks.

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English version:
St. Petersburg Mathematical Journal, 2017, 28:5, 569–596

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Received: 22.06.2015
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Citation: 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

Citation in format AMSBIB
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\paper Asymptotics of parabolic Green's functions on lattices
\jour Algebra i Analiz
\yr 2016
\vol 28
\issue 5
\pages 21--60
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\transl
\jour St. Petersburg Math. J.
\yr 2017
\vol 28
\issue 5
\pages 569--596
\crossref{https://doi.org/10.1090/spmj/1464}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. P. Gurevich, S. Tikhomirov, “Rattling in spatially discrete diffusion equations with hysteresis”, Multiscale Model. Simul., 15:3 (2017), 1176–1197  crossref  mathscinet  isi
    2. P. Gurevich, S. Tikhomirov, “Spatially discrete reaction-diffusion equations with discontinuous hysteresis”, Ann. Inst. Henri Poincare-Anal. Non Lineaire, 35:4 (2018), 1041–1077  crossref  mathscinet  zmath  isi  scopus
    3. Gurevich P., “Asymptotics of the Heat Kernels on 2D Lattices”, Asymptotic Anal., 112:1-2 (2019), 107–124  crossref  mathscinet  isi  scopus
  • Алгебра и анализ St. Petersburg Mathematical Journal
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