Abstract:
In this paper we study numerical approximations for positive solutions of a nonlinear heat equation with a nonlinear boundary condition. We describe in terms of the nonlinearities when solutions of a semidiscretization in space exist globally in time and when they blow up in finite time. We also find the blow-up rates and the blow-up sets. In particular we prove that regional blow-up is not reproduced by the numerical scheme. However, in the appropriate variables we can reproduce the correct blow-up set when the mesh parameter goes to zero.
Registro:
Documento: |
Artículo
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Título: | Numerical blow-up for a nonlinear problem with a nonlinear boundary condition |
Autor: | Ferreira, R.; Groisman, P.; Rossi, J.D. |
Filiación: | Universidad Autónoma de Madrid, 28049 Madrid, Spain Universidad de San Andrés, Vito Dumas 284 (1644), Victoria, Buenos Aires, Argentina Departamento de Matemática, FCEyN, UBA 1428, Argentina
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Palabras clave: | Nonlinear boundary conditions; Numerical blow-up; Porous medium equation |
Año: | 2002
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Volumen: | 12
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Número: | 4
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Página de inicio: | 461
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Página de fin: | 483
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DOI: |
http://dx.doi.org/10.1142/S021820250200174X |
Título revista: | Mathematical Models and Methods in Applied Sciences
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Título revista abreviado: | Math. Models Methods Appl. Sci.
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ISSN: | 02182025
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Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02182025_v12_n4_p461_Ferreira |
Referencias:
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Citas:
---------- APA ----------
Ferreira, R., Groisman, P. & Rossi, J.D.
(2002)
. Numerical blow-up for a nonlinear problem with a nonlinear boundary condition. Mathematical Models and Methods in Applied Sciences, 12(4), 461-483.
http://dx.doi.org/10.1142/S021820250200174X---------- CHICAGO ----------
Ferreira, R., Groisman, P., Rossi, J.D.
"Numerical blow-up for a nonlinear problem with a nonlinear boundary condition"
. Mathematical Models and Methods in Applied Sciences 12, no. 4
(2002) : 461-483.
http://dx.doi.org/10.1142/S021820250200174X---------- MLA ----------
Ferreira, R., Groisman, P., Rossi, J.D.
"Numerical blow-up for a nonlinear problem with a nonlinear boundary condition"
. Mathematical Models and Methods in Applied Sciences, vol. 12, no. 4, 2002, pp. 461-483.
http://dx.doi.org/10.1142/S021820250200174X---------- VANCOUVER ----------
Ferreira, R., Groisman, P., Rossi, J.D. Numerical blow-up for a nonlinear problem with a nonlinear boundary condition. Math. Models Methods Appl. Sci. 2002;12(4):461-483.
http://dx.doi.org/10.1142/S021820250200174X