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

 

Blow-up vs. spurious steady solutions


Authors: Julián Fernández Bonder and Julio D. Rossi
Journal: Proc. Amer. Math. Soc. 129 (2001), 139-144
MSC (1991): Primary 35K55, 35B40, 65M20
Published electronically: June 21, 2000
MathSciNet review: 1712866
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Abstract:

In this paper, we study the blow-up problem for positive solutions of a semidiscretization in space of the heat equation in one space dimension with a nonlinear flux boundary condition and a nonlinear absorption term in the equation. We obtain that, for a certain range of parameters, the continuous problem has blow-up solutions but the semidiscretization does not and the reason for this is that a spurious attractive steady solution appears.


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Additional Information

Julián Fernández Bonder
Affiliation: Departamento de Matemática, F.C.E y N., UBA, (1428) Buenos Aires, Argentina
Email: jfbonder@mate.dm.uba.ar

Julio D. Rossi
Affiliation: Departamento de Matemática, F.C.E y N., UBA, (1428) Buenos Aires, Argentina
Email: jrossi@mate.dm.uba.ar

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05663-X
PII: S 0002-9939(00)05663-X
Keywords: Blow-up, semidiscretization, spurious solutions
Received by editor(s): March 10, 1999
Published electronically: June 21, 2000
Additional Notes: This research was partially supported by Universidad de Buenos Aires under grant TX047 and by ANPCyT PICT No. 03-00000-00137. The second author was is also partially supported by Fundación Antorchas.
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2000 American Mathematical Society