WIAS Preprint No. 495, (1999)

Singularly perturbed reaction - diffusionsystems in case of exchange of stabilities


  • Butuzov, Valentin F.
  • Nefedov, Nikolai N.
  • Schneider, Klaus R.

2010 Mathematics Subject Classification

  • 34D15 34E05 92E20


  • Singular perturbation, asymptotic methods, upper and lower solutions, jumping behavior of reaction rates




We study singularly perturbed elliptic and parabolic differential equations under the assumption that the associated equation has intersecting families of equilibria (exchange of stabilities). We prove by means of the method of asymptotic lower and upper solutions that the asymptotic behavior with respect to the small parameter changes near the curve of exchange of stabilities. The application of that result to systems modelling fast bimolecular reactions in a heterogeneous environment implies a transition layer (jumping behavior) of the reaction rate. This behavior has to be taken into account for identification problems in reaction systems.

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