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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 1110-757X 1687-0042 |