The Fujita exponent for finite difference approximations of nonlocal and local semilinear blow-up problems

Fuente: arXiv
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Main Authors: del Teso, Félix, Ferreira, Raúl
Format: Preprint
Published: 2024
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_version_ 1866912458575183872
author del Teso, Félix
Ferreira, Raúl
author_facet del Teso, Félix
Ferreira, Raúl
contents We study monotone finite difference approximations for a broad class of reaction-diffusion problems, incorporating general symmetric Lévy operators. By employing an adaptive time-stepping discretization, we derive the discrete Fujita critical exponent for these problems. Additionally, under general consistency assumptions, we establish the convergence of discrete blow-up times to their continuous counterparts. As complementary results, we also present the asymptotic-in-time behavior of discrete heat-type equations as well as an extensive analysis of discrete eigenvalue problems.
format Preprint
id arxiv_https___arxiv_org_abs_2410_10458
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle The Fujita exponent for finite difference approximations of nonlocal and local semilinear blow-up problems
del Teso, Félix
Ferreira, Raúl
Numerical Analysis
35B44, 35R09, 65M06
G.1.8; G.1.9
We study monotone finite difference approximations for a broad class of reaction-diffusion problems, incorporating general symmetric Lévy operators. By employing an adaptive time-stepping discretization, we derive the discrete Fujita critical exponent for these problems. Additionally, under general consistency assumptions, we establish the convergence of discrete blow-up times to their continuous counterparts. As complementary results, we also present the asymptotic-in-time behavior of discrete heat-type equations as well as an extensive analysis of discrete eigenvalue problems.
title The Fujita exponent for finite difference approximations of nonlocal and local semilinear blow-up problems
topic Numerical Analysis
35B44, 35R09, 65M06
G.1.8; G.1.9
url https://arxiv.org/abs/2410.10458