Lack of smoothing for bounded solutions of a semilinear parabolic equation
classification
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keywords
singularitysolutionsboundedequationparabolicsemilinearconvergedomain
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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 $t\to\infty$.
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