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.
| Documento: | Artículo |
| Título: | Numerical blow-up for the porous medium equation with a source |
| Autor: | Ferreira, R.; Groisman, P.; Rossi, J.D. |
| Filiación: | Departamento de Matemáticas, U. Autónoma de Madrid, 28049 Madrid, Spain Departamento de Matemática, F.C.E y N., UBA, (1428) Buenos Aires, Argentina U. Carlos III de Madrid, 28911 Leganés, Madrid, Spain |
| Palabras clave: | Numerical blow-up; Porous medium equation |
| Año: | 2004 |
| Volumen: | 20 |
| Número: | 4 |
| Página de inicio: | 552 |
| Página de fin: | 575 |
| DOI: | http://dx.doi.org/10.1002/num.10103 |
| Título revista: | Numerical Methods for Partial Differential Equations |
| Título revista abreviado: | Numer Methods Partial Differential Equations |
| ISSN: | 0749159X |
| CODEN: | NMPDE |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0749159X_v20_n4_p552_Ferreira |
