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1996 Interior gradient blow-up in a semilinear parabolic equation
Sigurd B. Angenent, Marek Fila
Differential Integral Equations 9(5): 865-877 (1996).

Abstract

We present a one-dimensional semilinear parabolic equation for which the spatial derivative of solutions becomes unbounded in finite time while the solutions themselves remain bounded. In our example the derivative blows up in the interior of the space interval rather than at the boundary, as in earlier examples. In the case of monotone solutions we show that gradient blow-up occurs at a single point, and we study the shape of the singularity. Our argument for gradient blow-up also provides a pair of "naive viscosity sub- and super-solutions" which violate the comparison principle.

Citation

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Sigurd B. Angenent. Marek Fila. "Interior gradient blow-up in a semilinear parabolic equation." Differential Integral Equations 9 (5) 865 - 877, 1996.

Information

Published: 1996
First available in Project Euclid: 6 May 2013

zbMATH: 0864.35052
MathSciNet: MR1392084

Subjects:
Primary: 35K57
Secondary: 35B05, 35B35

Rights: Copyright © 1996 Khayyam Publishing, Inc.

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Vol.9 • No. 5 • 1996
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