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A degenerate reaction diffusion system modelling an optical biosensor

  • S. Merino
  • M. Grinfeld
  • S. McKee
Article

Abstract.

We investigate qualitative properties of a global semiflow associated with a degenerate reaction diffusion system with nonlinear boundary conditions. The system models an optical biosensor. By defining a suitable Liapunov function it is possible to give a complete description of the long time behaviour of the solutions. Indeed, we are able to prove that positive solutions converge to a single spatially homogeneous equilibrium state.

Key words. Degenerate reaction-diffusion system, chemical reaction networks, asymptotic behaviour. 

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Copyright information

© Birkhäuser Verlag, Basel, 1998

Authors and Affiliations

  • S. Merino
    • 1
  • M. Grinfeld
    • 2
  • S. McKee
    • 2
  1. 1.Heriot-Watt University, Dept. of Mathematics, Riccarton Campus, Edinburgh, EH14 4AS, UK, e-mail: sandro@ma.hw.ac.ukUK
  2. 2.University of Strathclyde, Dept. of Mathematics, Livingstone Tower 26, Richmond Street, Glasgow, G1 1XH, UK, e-mail: caas@ccsun.strath.ac.ukUK

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