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Lack of smoothing for bounded solutions of a semilinear parabolic equation. (English) Zbl 1436.35243

Summary: 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 \(t \rightarrow \infty\).

MSC:

35K58 Semilinear parabolic equations
35B44 Blow-up in context of PDEs
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