ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. 67, 1 (1998)
pp. 83-100

WAVE BIFURCATION IN MODELS FOR HETEROGENEOUS CATALYSIS
S. KROMKER

Abstract. Heterogeneous Catalysis means that the reacting species and the catalyst do not have the same phase. A mathematical model for such a reaction has to take into account as well the complex kinetic processes and the spatial coupling. Depending on how strong the reactants are bound to the surface of the catalyst, the diffusion coefficients may vary by orders. Diffusion does not only smoothen the concentration gradients which are given by the initial data or result from the reaction kinetic processes. It is also able to induce instabilities which give rise to stable inhomogeneous steady or time-periodic solutions. The conditions for such a bifurcation are rather restrictive but can be checked by only considering the kinetic part. Numerical simulations can be carried out more precisely in the neighborhood of the critical parameters.

AMS subject classification. 35K57; Secondary 35B10, 35B22, 58F40
Keywords. Hopf bifurcation, spatio-temporal pattern formation, cubic autocatalysis

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Acta Mathematica Universitatis Comenianae
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