Singular solutions of some nonlinear parabolic equations with spatially inhomogeneous absorption

2007/08/06 by Andrey Shishkov, Shishkov, Andrey, Laurent Veron +1
Engineering · Mathematics · #35K60 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Fluid Dynamics and Thin Films #Nonlinear Differential Equations Analysis #Nonlinear Partial Differential Equations #math.AP #math.CA #msc:35K60

paper · pdf · doi:10.48550/arxiv.0708.0756

29 pages

openalex publication_date 2007/08/06 · arxiv created 2007/08/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the limit behaviour of solutions of a class of solutions of nonlinear parabolic equations with a degenerate strong absorption. We prove that two types of phenomena can occur: the pointwise singularity or the formation of razor blades (or persistent singularities).

Citations

• Long-time extinction of solutions of some semilinear parabolic equations

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