Numerical blow-up for the porous medium equation with a source
We study numerical approximations of positive solutions of the porous medium equation with a nonlinear source, {ut = (um) xx + up, (x, t) ∈ (-L, L) × (0, T), u(-L, t) = u(L, t) = 1, t∈ [0, t), u(x, 0) = φ(x), ≥1 x ∈ (-L, L), where m > 1, p > 0 and L > 0 are parameters. We descri...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0749159X_v20_n4_p552_Ferreira |
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todo:paper_0749159X_v20_n4_p552_Ferreira2023-10-03T15:39:34Z Numerical blow-up for the porous medium equation with a source Ferreira, R. Groisman, P. Rossi, J.D. Numerical blow-up Porous medium equation We study numerical approximations of positive solutions of the porous medium equation with a nonlinear source, {ut = (um) xx + up, (x, t) ∈ (-L, L) × (0, T), u(-L, t) = u(L, t) = 1, t∈ [0, t), u(x, 0) = φ(x), ≥1 x ∈ (-L, L), where m > 1, p > 0 and L > 0 are parameters. We describe in terms of p, m, and L when solutions of a semidiscretization in space exist globally in time and when they blow up in a finite time. We also find the blow-up rates and the blow-up sets, proving that there is no regional blow-up for the numerical scheme. © 2004 Wiley Periodicals, Inc. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0749159X_v20_n4_p552_Ferreira |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Numerical blow-up Porous medium equation |
| spellingShingle |
Numerical blow-up Porous medium equation Ferreira, R. Groisman, P. Rossi, J.D. Numerical blow-up for the porous medium equation with a source |
| topic_facet |
Numerical blow-up Porous medium equation |
| description |
We study numerical approximations of positive solutions of the porous medium equation with a nonlinear source, {ut = (um) xx + up, (x, t) ∈ (-L, L) × (0, T), u(-L, t) = u(L, t) = 1, t∈ [0, t), u(x, 0) = φ(x), ≥1 x ∈ (-L, L), where m > 1, p > 0 and L > 0 are parameters. We describe in terms of p, m, and L when solutions of a semidiscretization in space exist globally in time and when they blow up in a finite time. We also find the blow-up rates and the blow-up sets, proving that there is no regional blow-up for the numerical scheme. © 2004 Wiley Periodicals, Inc. |
| format |
JOUR |
| author |
Ferreira, R. Groisman, P. Rossi, J.D. |
| author_facet |
Ferreira, R. Groisman, P. Rossi, J.D. |
| author_sort |
Ferreira, R. |
| title |
Numerical blow-up for the porous medium equation with a source |
| title_short |
Numerical blow-up for the porous medium equation with a source |
| title_full |
Numerical blow-up for the porous medium equation with a source |
| title_fullStr |
Numerical blow-up for the porous medium equation with a source |
| title_full_unstemmed |
Numerical blow-up for the porous medium equation with a source |
| title_sort |
numerical blow-up for the porous medium equation with a source |
| url |
http://hdl.handle.net/20.500.12110/paper_0749159X_v20_n4_p552_Ferreira |
| work_keys_str_mv |
AT ferreirar numericalblowupfortheporousmediumequationwithasource AT groismanp numericalblowupfortheporousmediumequationwithasource AT rossijd numericalblowupfortheporousmediumequationwithasource |
| _version_ |
1782024692062748672 |