Similarity solutions of nonlinear diffusion problems related to mathematical hydraulics and the fokker-planck equation

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Abstract

Self-similar solutions of a nonlinear differential equation obtained by generalizing the relation employed in hydraulics to model the resistances in open channel flow were studied. The resulting model encompassed various particular cases in diverse physical phenomena, such as gravity currents, creeping flows of Newtonian and non-Newtonian fluids and nonlinear Fokker-Planck equations. Solutions of both source-type and dam-break problems were also studied. Closed-form solutions were discussed along with a qualitative study of two phase-plane formulations based on two different variable transformations.

Original languageEnglish (US)
Article number056303
Pages (from-to)056303-1-056303-8
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume70
Issue number5 2
DOIs
StatePublished - Nov 2004

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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