arXiv:1107.2153 Abstract | arXiv Analytics

arXiv:1107.2153 [math.AP]Abstract References Reviews Resources

Total Variation Flow and Sign Fast Diffusion in one dimension

Published 2011-07-11, updated 2011-08-17Version 2

We consider the dynamics of the Total Variation Flow (TVF) $u_t=\div(Du/|Du|)$ and of the Sign Fast Diffusion Equation (SFDE) $u_t=\Delta\sign(u)$ in one spatial dimension. We find the explicit dynamic and sharp asymptotic behaviour for the TVF, and we deduce the one for the SFDE by an explicit correspondence between the two equations.

DOI: 10.1016/j.jde.2012.01.003

Categories: math.AP

Subjects: 35K55, 35K59, 35K67, 35K92, 35B40

Keywords: total variation flow, sign fast diffusion equation, sharp asymptotic behaviour, explicit correspondence, spatial dimension

Tags: journal article

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