Lack of smoothing for bounded solutions of a semilinear parabolic\n equation

2019/03/21 by Марек Фила, Fila, Marek, Johannes Lankeit +1
Engineering · Mathematics · #35B44 #35K58 #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1903.08899

openalex publication_date 2019/03/21 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

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

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