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Abstract:

We study the asymptotic behavior of a semi-discrete numerical approximation for a pair of heat equations ut = Δu, vt = Δv in Ω × (0, T); fully coupled by the boundary conditions ∂u/∂η = up11vp12, ∂v/∂η = up21vp22 on ∂Ω × (0, T), where Ω is a bounded smooth domain in ℝd. We focus in the existence or not of non-simultaneous blow-up for a semi-discrete approximation (U, V). We prove that if U blows up in finite time then V can fail to blow up if and only if p11 > 1 and p21 < 2(p11 - 1), which is the same condition as the one for non-simultaneous blow-up in the continuous problem. Moreover, we find that if the continuous problem has non-simultaneous blow-up then the same is true for the discrete one. We also prove some results about the convergence of the scheme and the convergence of the blow-up times.

Registro:

Documento: Artículo
Título:Simultaneous vs. non-simultaneous blow-up in numerical approximations of a parabolic system with non-linear boundary conditions
Autor:Acosta, G.; Bonder, J.F.; Groisman, P.; Rossi, J.D.
Filiación:Instituto de Ciencias, Univ. Nac. Gral. Sarmiento, J.M. Gutierrez entre Verdi y J.L. Suarez, (1613) Los Polvorines, Buenos Aires, Argentina
Departamento de Matemática, FCEyN, UBA, (1428), Buenos Aires, Argentina
Universidad de San Andrés, Vito Dumas 284, (1644), Victoria, Buenos Aires, Argentina
Palabras clave:Asymptotic behavior; Blow-up; Non-linear boundary conditions; Parabolic equations; Semi-discretization in space
Año:2002
Volumen:36
Número:1
Página de inicio:55
Página de fin:68
DOI: http://dx.doi.org/10.1051/m2an:2002003
Título revista:Mathematical Modelling and Numerical Analysis
Título revista abreviado:Math. Model. Numer. Anal.
ISSN:0764583X
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_0764583X_v36_n1_p55_Acosta.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0764583X_v36_n1_p55_Acosta

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Citas:

---------- APA ----------
Acosta, G., Bonder, J.F., Groisman, P. & Rossi, J.D. (2002) . Simultaneous vs. non-simultaneous blow-up in numerical approximations of a parabolic system with non-linear boundary conditions. Mathematical Modelling and Numerical Analysis, 36(1), 55-68.
http://dx.doi.org/10.1051/m2an:2002003
---------- CHICAGO ----------
Acosta, G., Bonder, J.F., Groisman, P., Rossi, J.D. "Simultaneous vs. non-simultaneous blow-up in numerical approximations of a parabolic system with non-linear boundary conditions" . Mathematical Modelling and Numerical Analysis 36, no. 1 (2002) : 55-68.
http://dx.doi.org/10.1051/m2an:2002003
---------- MLA ----------
Acosta, G., Bonder, J.F., Groisman, P., Rossi, J.D. "Simultaneous vs. non-simultaneous blow-up in numerical approximations of a parabolic system with non-linear boundary conditions" . Mathematical Modelling and Numerical Analysis, vol. 36, no. 1, 2002, pp. 55-68.
http://dx.doi.org/10.1051/m2an:2002003
---------- VANCOUVER ----------
Acosta, G., Bonder, J.F., Groisman, P., Rossi, J.D. Simultaneous vs. non-simultaneous blow-up in numerical approximations of a parabolic system with non-linear boundary conditions. Math. Model. Numer. Anal. 2002;36(1):55-68.
http://dx.doi.org/10.1051/m2an:2002003