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Blow-up for semidiscretization of a localized semilinear heat equation

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This paper concerns the study of the numerical approximation for the following initial-boundary value problem:[wzór] where f: [0, ∞) → [0, ∞) is a C2 convex, nondecreasing function,(wzór) and ε is a positive parameter. Under some assumptions, we prove that the solution of a semidiscrete form of the above problem blows up in a finite time and estimate its semidiscrete blow-up time. We also show that the semidiscrete blow-up time in certain cases converges to the real one when the mesh size tends to zero. Finally, we give some numerical experiments to illustrate our analysis.
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Bibliogr. 25 poz.
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