Numerical Blow-Up Time for a Semilinear Parabolic Equation with Nonlinear Boundary Conditions
We obtain some conditions under which the positive solution for semidiscretizations of the semilinear equation ut=uxx−a(x,t)f(u), 0<x<1, t∈(0,T), with boundary conditions ux(0,t)=0, ux(1,t)=b(t)g(u(1,t)), blows up in a finite time and estimate its semidiscrete blow-up time. We also establish...
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2008/753518 |
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| author | Louis A. Assalé Théodore K. Boni Diabate Nabongo |
| author_facet | Louis A. Assalé Théodore K. Boni Diabate Nabongo |
| author_sort | Louis A. Assalé |
| collection | DOAJ |
| description | We obtain some conditions under which the positive solution for
semidiscretizations of the semilinear equation ut=uxx−a(x,t)f(u), 0<x<1, t∈(0,T), with boundary conditions ux(0,t)=0, ux(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. |
| format | Article |
| id | doaj-art-4c2648849d234297aa733c3fdd1d5b6c |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-4c2648849d234297aa733c3fdd1d5b6c2025-02-03T01:09:27ZengWileyJournal of Applied Mathematics1110-757X1687-00422008-01-01200810.1155/2008/753518753518Numerical Blow-Up Time for a Semilinear Parabolic Equation with Nonlinear Boundary ConditionsLouis A. Assalé0Théodore K. Boni1Diabate Nabongo2Institut National Polytechnique Houphouët-Boigny de Yamoussoukro, BP 1093, Yamoussoukro, Cote D'IvoireInstitut National Polytechnique Houphouët-Boigny de Yamoussoukro, BP 1093, Yamoussoukro, Cote D'IvoireDépartement de Mathématiques et Informatiques, Université d'Abobo-Adjamé, UFR-SFA, 16 BP 372 Abidjan 16, Cote D'IvoireWe obtain some conditions under which the positive solution for semidiscretizations of the semilinear equation ut=uxx−a(x,t)f(u), 0<x<1, t∈(0,T), with boundary conditions ux(0,t)=0, ux(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.http://dx.doi.org/10.1155/2008/753518 |
| spellingShingle | Louis A. Assalé Théodore K. Boni Diabate Nabongo Numerical Blow-Up Time for a Semilinear Parabolic Equation with Nonlinear Boundary Conditions Journal of Applied Mathematics |
| title | Numerical Blow-Up Time for a Semilinear Parabolic Equation with Nonlinear Boundary Conditions |
| title_full | Numerical Blow-Up Time for a Semilinear Parabolic Equation with Nonlinear Boundary Conditions |
| title_fullStr | Numerical Blow-Up Time for a Semilinear Parabolic Equation with Nonlinear Boundary Conditions |
| title_full_unstemmed | Numerical Blow-Up Time for a Semilinear Parabolic Equation with Nonlinear Boundary Conditions |
| title_short | Numerical Blow-Up Time for a Semilinear Parabolic Equation with Nonlinear Boundary Conditions |
| title_sort | numerical blow up time for a semilinear parabolic equation with nonlinear boundary conditions |
| url | http://dx.doi.org/10.1155/2008/753518 |
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