an:06965745
Zbl 1401.35191
Yang, Wenbin; Wei, Zhaoying; Jiang, Hongling; Li, Haixia; Li, Yanling
The existence of steady states for a bimolecular model with autocatalysis and saturation law
EN
Z. Angew. Math. Phys. 69, No. 5, Paper No. 131, 19 p. (2018).
00418238
2018
j
35K57 35B35
bimolecular model; autocatalysis and saturation law; positive steady state; existence and nonexistence; bifurcation; degree theory
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.