Total Variation Flow and Sign Fast Diffusion in one dimension

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:252

Article

Bonforte, Matteo¹  Figalli, Alessio² 

[1] Univ Autonoma Madrid, Dept Matemat, E-28049 Madrid, Spain

[2] Univ Texas Austin, Dept Math, Austin, TX 78712 USA

关键词: Fast Diffusion;    Total Variation Flow;    Asymptotic;    Extinction profile;    Convergence rates;    Extinction time;   

DOI  :  10.1016/j.jde.2012.01.003

来源: Elsevier

【 摘 要 】

We consider the dynamics of the Total Variation Flow (TVF) u(t) = div(Du/vertical bar Du vertical bar) 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. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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