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The existence of steady states for a bimolecular model with autocatalysis and saturation law. (English) Zbl 1401.35191
Summary: In this paper, a reaction-diffusion system known as a bimolecular model with autocatalysis and saturation law is considered. Firstly, we briefly obtain some characterizations for the positive solutions, including the a priori estimate of the positive solutions and the nonexistence of non-constant positive solution. Secondly, we emphatically discusses the bifurcation from the unique positive constant solution with both simple eigenvalues and double eigenvalues in one-dimensional case. Meanwhile, some other existence results are shown to supplement the analytical conclusions with the degree theory in \(N\) dimensional case.
MSC:
35K57 Reaction-diffusion equations
35B35 Stability in context of PDEs
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