Blow-up vs. spurious steady solutions
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- by Julián Fernández Bonder and Julio D. Rossi PDF
- Proc. Amer. Math. Soc. 129 (2001), 139-144 Request permission
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.References
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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
- MR Author ID: 601009
- ORCID: 0000-0001-7622-2759
- Email: jrossi@mate.dm.uba.ar
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 139-144
- MSC (1991): Primary 35K55, 35B40, 65M20
- DOI: https://doi.org/10.1090/S0002-9939-00-05663-X
- MathSciNet review: 1712866