## Adaptivity and Blow-Up Detection for Nonlinear Evolution Problems

- Andrea Cangiani, Emmanuil H. Georgoulis, Irene Kyza, Stephen Metcalfe
- SIAM J. Scientific Computing
- 2016

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@article{Assal2008NumericalBT, title={Numerical Blow-Up Time for a Semilinear Parabolic Equation with Nonlinear Boundary Conditions}, author={Louis A. Assal{\'e} and Th{\'e}odore K. Boni and Diabate Nabongo}, journal={J. Applied Mathematics}, year={2008}, volume={2008} }

- Published 2008 in J. Applied Mathematics
DOI:10.1155/2008/753518

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… CONTINUE READING