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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On numerical blow-up sets


Authors: Julián Fernández Bonder, Pablo Groisman and Julio D. Rossi
Journal: Proc. Amer. Math. Soc. 130 (2002), 2049-2055
MSC (2000): Primary 35K55, 35B40, 65M20
Published electronically: January 17, 2002
MathSciNet review: 1896041
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Abstract: In this paper we study numerical blow-up sets for semidicrete approximations of the heat equation with nonlinear boundary conditions. We prove that the blow-up set either concentrates near the boundary or is the whole domain.


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Additional Information

Julián Fernández Bonder
Affiliation: Departamento de Matemática, FCEyN, UBA (1428) Buenos Aires, Argentina
Email: jfbonder@dm.uba.ar

Pablo Groisman
Affiliation: Departamento de Matemática, FCEyN, UBA (1428) Buenos Aires, Argentina
Address at time of publication: Departamento de Matemática y Ciencias, Universidad de San Andrés, Vito Dumas 284 (B1D1644)–Victoria, Buenos Aires, Argentina
Email: pgroisma@dm.uba.ar, pablog@udesa.edu.ar

Julio D. Rossi
Affiliation: Departamento de Matemática, FCEyN, UBA (1428) Buenos Aires, Argentina
Email: jrossi@dm.uba.ar

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06350-5
PII: S 0002-9939(02)06350-5
Keywords: Numerical approximations, nonlinear boundary conditions
Received by editor(s): September 19, 2000
Received by editor(s) in revised form: February 7, 2001
Published electronically: January 17, 2002
Additional Notes: This work was partially supported by Universidad de Buenos Aires under grants TX47 and TX48 and by ANPCyT PICT No. 03-00000-00137. The third author was also supported by Fundación Antorchas.
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2002 American Mathematical Society