Convergence to a singular steady state of a parabolic equation with gradient blow-up

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Abstract

We study solutions of a parabolic equation which are bounded but whose spatial derivatives blow up in finite time. We establish results on the behavior on the lateral boundary where the singularity occurs and on the rate of convergence to a singular steady state.

Keywords

Semilinear parabolic equation
Gradient blow-up
Rate of convergence to a steady state

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