Artículo
Quirós, F.; Rossi, J.D. "Blow-up sets for linear diffusion equations in one dimension" (2004) Zeitschrift fur Angewandte Mathematik und Physik. 55(2):357-362
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Abstract:
We consider the heat equation in the half-line with Dirichlet boundary data which blow up in finite time. Though the blow-up set may be any interval [0, a], a ∈ [0, ∞], depending on the Dirichlet data, we prove that the effective blow-up set, that is, the set of points x ≥ 0 where the solution behaves like u(0, t), consists always only of the origin. As an application of our results we consider a system of two heat equations with a nontrivial nonlinear flux coupling at the boundary. We show that by prescribing the non-linearities the two components may have different blow-up sets. However, the effective blow-up sets do not depend on the coupling and coincide with the origin for both components.
Registro:
| Documento: | Artículo |
| Título: | Blow-up sets for linear diffusion equations in one dimension |
| Autor: | Quirós, F.; 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 Fac. de Matemáticas, Universidad Católica de Chile, Av. Vicuña Mackenna 4860, Macul, Santiago, Chile |
| Palabras clave: | Blow-up sets; Heat equation; Nonlinear boundary conditions |
| Año: | 2004 |
| Volumen: | 55 |
| Número: | 2 |
| Página de inicio: | 357 |
| Página de fin: | 362 |
| DOI: | http://dx.doi.org/10.1007/s00033-003-2102-z |
| Título revista: | Zeitschrift fur Angewandte Mathematik und Physik |
| Título revista abreviado: | Z. Angew. Math. Phys. |
| ISSN: | 00442275 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00442275_v55_n2_p357_Quiros |
Referencias:
- Bandle, C., Brunner, H., Blowup in diffusion equations: A survey (1998) J. Comput. Appl. Math., 97, pp. 3-22
- Fernández Bonder, J., Rossi, J.D., Asymptotic behaviour for a parabolic system with nonlinear boundary conditions (2000) Collect. Math., 51, pp. 285-308
- Galaktionov, V.A., Vázquez, J.L., The problem of blow-up in nonlinear parabolic equations. Current developments in partial differential equations (Temuco, 1999) (2002) Discrete Contin. Dyn. Syst., 8, pp. 399-433
- Gilding, B.H., Herrero, M.A., Localization and blow-up of thermal waves in nonlinear heat conduction with peaking (1988) Math. Ann., 282, pp. 223-242
- Groisman, P., Rossi, J.D., Asymptotic behaviour for a numerical approximation of a parabolic problem with blowing up solutions (2001) J. Comput. Appl. Math., 135, pp. 135-155
- Quirós, F., Rossi, J.D., Blow-up seta and Fujita type curves for a degenerate parabolic system with nonlinear boundary conditions (2001) Indiana Univ. Math. J., 50, pp. 629-654
- Samarskii, A.A., Galaktionov, V.A., Kurdyumov, S.P., Mikhailov, A.P., (1987) Blow-up in Quasilinear Parabolic Equations, , Nauka, Moscow,(in Russian)
- (1995) Gruyter Expositions in Mathematics, 19. , English transi.: Walter de Gruyter & Co., Berlin
Citas:
---------- APA ----------
Quirós, F. & Rossi, J.D. (2004) . Blow-up sets for linear diffusion equations in one dimension. Zeitschrift fur Angewandte Mathematik und Physik, 55(2), 357-362.http://dx.doi.org/10.1007/s00033-003-2102-z
---------- CHICAGO ----------
Quirós, F., Rossi, J.D. "Blow-up sets for linear diffusion equations in one dimension" . Zeitschrift fur Angewandte Mathematik und Physik 55, no. 2 (2004) : 357-362.http://dx.doi.org/10.1007/s00033-003-2102-z
---------- MLA ----------
Quirós, F., Rossi, J.D. "Blow-up sets for linear diffusion equations in one dimension" . Zeitschrift fur Angewandte Mathematik und Physik, vol. 55, no. 2, 2004, pp. 357-362.http://dx.doi.org/10.1007/s00033-003-2102-z
---------- VANCOUVER ----------
Quirós, F., Rossi, J.D. Blow-up sets for linear diffusion equations in one dimension. Z. Angew. Math. Phys. 2004;55(2):357-362.http://dx.doi.org/10.1007/s00033-003-2102-z
