Lack of smoothing for bounded solutions of a semilinear parabolic equation

Abstract

We study a semilinear parabolic equation that possesses global bounded weak solutions whose gradient has a singularity in the interior of the domain for all t > 0. The singularity of these solutions is of the same type as the singularity of a stationary solution to which they converge as t → ∞.

Keywords

• singular gradient
• semilinear parabolic equation
• 35k58
• 35b44