Journal of Applied Mathematics

Numerical Blow-Up Time for a Semilinear Parabolic Equation with Nonlinear Boundary Conditions

Louis A. Assalé, Théodore K. Boni, and Diabate Nabongo

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Abstract

We obtain some conditions under which the positive solution for semidiscretizations of the semilinear equation u t = u x x a ( x , t ) f ( u ) , 0 < x < 1 , t ( 0 , T ) , with boundary conditions u x ( 0 , t ) = 0 , u x ( 1 , t ) = b ( t ) g ( u ( 1 , t ) ) , blows up in a finite time and estimate its semidiscrete blow-up time. We also establish the convergence of the semidiscrete blow-up time and obtain some results about numerical blow-up rate and set. Finally, we get an analogous result taking a discrete form of the above problem and give some computational results to illustrate some points of our analysis.

Article information

Source
J. Appl. Math., Volume 2008 (2008), Article ID 753518, 29 pages.

Dates
First available in Project Euclid: 2 March 2010

Permanent link to this document
https://projecteuclid.org/euclid.jam/1267538643

Digital Object Identifier
doi:10.1155/2008/753518

Zentralblatt MATH identifier
1179.35168

Citation

Assalé, Louis A.; Boni, Théodore K.; Nabongo, Diabate. Numerical Blow-Up Time for a Semilinear Parabolic Equation with Nonlinear Boundary Conditions. J. Appl. Math. 2008 (2008), Article ID 753518, 29 pages. doi:10.1155/2008/753518. https://projecteuclid.org/euclid.jam/1267538643


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