Qualitative analysis of steady states to the Sel'kov model |
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Authors: | Rui Peng |
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Institution: | Institute of Nonlinear Complex Systems, College of Science, China Three Gorges University, Yichang City 443002, Hubei Province, PR China |
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Abstract: | In this work, we are concerned with a reaction-diffusion system well known as the Sel'kov model, which has been used for the study of morphogenesis, population dynamics and autocatalytic oxidation reactions. We derive some further analytic results for the steady states to this model. In particular, we show that no nonconstant positive steady state exists if 0<p?1 and θ is large, which provides a sharp contrast to the case of p>1 and large θ, where nonconstant positive steady states can occur. Thus, these conclusions indicate that the parameter p plays a crucial role in leading to spatially nonhomogeneous distribution of the two reactants. The a priori estimates are fundamental to our mathematical approaches. |
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Keywords: | 35J55 35B45 35Q80 92C15 92C40 |
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