MR2589658
Kumiko HATTORI and Tetsuya HATTORI
Kumiko HATTORI and Tetsuya HATTORI
Equation of Motion for Incompressible Mixed Fluid Driven by Evaporation and Its Application to Online Rankings
Funkcialaj Ekvacioj. Serio Internacia
52
2009
301--319
http://fe.math.kobe-u.ac.jp/FE/FullPapers/52-3/52_301.pdf
http://www.ams.org/mathscinet-getitem?mr=MR2589658
We consider a system of partial differential equations for the densities of components of one dimensional incompressible fluid mixture whose motion is driven by evaporation. We prove existence and give explicit form of unique global classical non-negative solution to initial value problem for the system. The solution is known to be an infinite particle limit of stochastic ranking processes, which is a simple stochastic model of time evolutions of Amazon Sales Ranks. As a practical application, we collected data from the web and performed statistical fits to our formula. The results suggest that the system of equations and solutions, though very simple, may have applications in the analysis of online rankings.
Evaporation driven fluid, Non-linear wave, Stochastic ranking process, Long tail, Online ranking.
Primary 35C05; Secondary 35Q35, 82C22.
52-301
2009
Equation of Motion for Incompressible Mixed Fluid Driven by Evaporation and Its Application to Online Rankings
Kumiko HATTORI and Tetsuya HATTORI
Kumiko HATTORI and Tetsuya HATTORI
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