The Fujita exponent for finite difference approximations of nonlocal and local semilinear blow-up problems
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912458575183872 |
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| 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 |
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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 |