Artículo
Acosta, G.; Bonder, J.F.; Groisman, P.; Rossi, J.D. "Numerical approximation of a parabolic problem with a nonlinear boundary condition in several space dimensions" (2002) Discrete and Continuous Dynamical Systems - Series B. 2(2):279-294
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Abstract:
In this paper we study the asymptotic behavior of a semidiscrete numerical approximation for the heat equation, ut = Δu, in a bounded smooth domain with a nonlinear flux boundary condition, ∂u/∂η = up. We focus in the behavior of blowing up solutions. We prove that every numerical solution blows up in finite time if and only if p > 1 and that the numerical blow-up time converges to the continuous one as the mesh parameter goes to zero. Also we show that the blow-up rate for the numerical scheme is different from the continuous one. Nevertheless we find that the blow-up set for the numerical approximations is contained in a small neighborhood of the blow-up set of the continuous problem when the mesh parameter is small enough.
Registro:
| Documento: | Artículo |
| Título: | Numerical approximation of a parabolic problem with a nonlinear boundary condition in several space dimensions |
| Autor: | Acosta, G.; Bonder, J.F.; Groisman, P.; Rossi, J.D. |
| Filiación: | Department of Mathematics, FCEyN Universidad de Buenos Aires, 1428 Buenos Aires, Argentina Institute de Ciencias, Univ. Nac. de Gral., Sarmiento J.M. G.V./S. (1613), Los Polvorines, Buenos Aires, Argentina |
| Palabras clave: | Asymptotic; Blow-up; Parabolic equations; Semidiscretization in space |
| Año: | 2002 |
| Volumen: | 2 |
| Número: | 2 |
| Página de inicio: | 279 |
| Página de fin: | 294 |
| Título revista: | Discrete and Continuous Dynamical Systems - Series B |
| Título revista abreviado: | Discrete Contin. Dyn. Syst. Ser. B |
| ISSN: | 15313492 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15313492_v2_n2_p279_Acosta |
Referencias:
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Citas:
---------- APA ----------
Acosta, G., Bonder, J.F., Groisman, P. & Rossi, J.D. (2002) . Numerical approximation of a parabolic problem with a nonlinear boundary condition in several space dimensions. Discrete and Continuous Dynamical Systems - Series B, 2(2), 279-294.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15313492_v2_n2_p279_Acosta [ ]
---------- CHICAGO ----------
Acosta, G., Bonder, J.F., Groisman, P., Rossi, J.D. "Numerical approximation of a parabolic problem with a nonlinear boundary condition in several space dimensions" . Discrete and Continuous Dynamical Systems - Series B 2, no. 2 (2002) : 279-294.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15313492_v2_n2_p279_Acosta [ ]
---------- MLA ----------
Acosta, G., Bonder, J.F., Groisman, P., Rossi, J.D. "Numerical approximation of a parabolic problem with a nonlinear boundary condition in several space dimensions" . Discrete and Continuous Dynamical Systems - Series B, vol. 2, no. 2, 2002, pp. 279-294.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15313492_v2_n2_p279_Acosta [ ]
---------- VANCOUVER ----------
Acosta, G., Bonder, J.F., Groisman, P., Rossi, J.D. Numerical approximation of a parabolic problem with a nonlinear boundary condition in several space dimensions. Discrete Contin. Dyn. Syst. Ser. B. 2002;2(2):279-294.Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15313492_v2_n2_p279_Acosta [ ]
