A River Water Quality Model for Time Varying BOD Discharge Concentration

Seth F. Oppenheimer, Donald Dean Adrian, Akram Alshawabkeh

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


We consider a model for biochemical oxygen demand (BOD) in a semi-infinite river where the BOD is prescribed by a time varying function at the left endpoint. That is, we study the problem with a time varying boundary loading. We obtain the well-posedness for the model when the boundary loading is smooth in time. We also obtain various qualitative results such as ordering, positivity, and boundedness. Of greatest interest, we show that a periodic loading function admits a unique asymptotically attracting periodic solution. For non-smooth loading functions, we obtain weak solutions. Finally, for certain special cases, we show how to obtain explicit solutions in the form of infinite series.

Original languageEnglish (US)
Pages (from-to)193-221
Number of pages29
JournalMathematical Problems in Engineering
Issue number3
StatePublished - 1999
Externally publishedYes


  • Convection-diffusion equations
  • Environmental modeling
  • Quasi-steady-state
  • River model
  • Weak solutions

ASJC Scopus subject areas

  • General Mathematics
  • General Engineering


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