Talk:Total variation diminishing

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The remark "For physically realisable systems where there is energy dissipation of some kind, the total variation does not increase with time." seems to be untrue. Example: A cylinder of liquid with surface tension and viscosity breaks up into droplets in finite time due to the Plateau–Rayleigh instability. Initially, the total variation of the liquid filament radius is zero, but it increases exponentially due to the instability. There is energy dissipation and the system can be physically realized. Not sure what we can say about this, though. Something seems to be bounded. I removed the comment for now, until we can fill it in. Greetings, --Roger Jeurissen (talk) 20:23, 23 June 2009 (UTC)[reply]