Well-posedness of sudden directional diffusion equations

2012/07/20 by Piotr Bogusław Mucha, Mucha, Piotr Bogusław, Piotr Rybka +1
Mathematics · #35K65 #35K67 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35K65 #msc:35K67

paper · pdf · doi:10.48550/arxiv.1207.4929

18 pages

arxiv created 2012/07/20 · arxiv updated 2012/07/23

Abstract

Our goal is to establish existence with suitable initial data of solutions to general parabolic equation in one dimension, u_t = L(u_x)_x, where L is merely a monotone function. We also expose the basic properties of solutions, concentrating on maximal possible regularity. Analysis of solutions with convex initial data explains why we may call them \it almost classical. Some qualitative aspects of solutions, like facets -- flat regions of solutions, are studied too.

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