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Эта публикация цитируется в 3 научных статьях (всего в 3 статьях)
Статьи
Asymptotics of parabolic Green's functions on lattices
P. Gurevichab a Free University of Berlin, Germany
b Peoples' Friendship University, Russia
Аннотация:
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.
Ключевые слова:
spatially discrete parabolic equations, asymptotics, discrete Green functions, lattice Green functions, heat kernels of lattices, continuous-time random walks.
Полный текст:
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Список литературы:
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Англоязычная версия:
St. Petersburg Mathematical Journal, 2017, 28:5, 569–596
Реферативные базы данных:
Тип публикации:
Статья Поступила в редакцию: 22.06.2015
Язык публикации: английский
Образец цитирования:
P. Gurevich, “Asymptotics of parabolic Green's functions on lattices”, Алгебра и анализ, 28:5 (2016), 21–60; St. Petersburg Math. J., 28:5 (2017), 569–596
Цитирование в формате AMSBIB
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Образцы ссылок на эту страницу:
http://mi.mathnet.ru/aa1506 http://mi.mathnet.ru/rus/aa/v28/i5/p21
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
Эта публикация цитируется в следующих статьяx:
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P. Gurevich, S. Tikhomirov, “Rattling in spatially discrete diffusion equations with hysteresis”, Multiscale Model. Simul., 15:3 (2017), 1176–1197
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P. Gurevich, S. Tikhomirov, “Spatially discrete reaction-diffusion equations with discontinuous hysteresis”, Ann. Inst. Henri Poincare-Anal. Non Lineaire, 35:4 (2018), 1041–1077
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Gurevich P., “Asymptotics of the Heat Kernels on 2D Lattices”, Asymptotic Anal., 112:1-2 (2019), 107–124
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