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Blow-up vs. spurious steady solutions
Author(s):
Julián
Fernández Bonder;
Julio
D.
Rossi
Journal:
Proc. Amer. Math. Soc.
129
(2001),
139-144.
MSC (1991):
Primary 35K55, 35B40, 65M20
Posted:
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.
References:
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- 2.
- M. Chipot, M. Fila and P. Quittner. Stationary solutions, blow up and convergence to stationary solutions for semilinear parabolic equations with nonlinear boundary conditions. Acta Math. Univ. Comenianae. Vol. LX, 1(1991), 35-103. MR 92h:35110
- 3.
- R. G. Duran, J. I. Etcheverry and J. D. Rossi. Numerical approximation of a parabolic problem with a nonlinear boundary condition. Disc. and Cont. Dyn. Sys., vol 4 (3), 1998, 497-506. MR 99a:65122
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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:
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
Posted:
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 of article:
Copyright
2000,
American Mathematical Society
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