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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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