Steady-state solution for a general Schnakenberg model
The author studies the Schnakenberg model of chemical reaction with limit cycle behaviour. The reactants are distributed in an isolated domain. The elliptic nonlinear system describes the steady-state distributions of the reactants. The boundary conditions are homogeneous Neumann conditions. This system has a unique constant solution. The author reveals the conditions (on the diffusivities of reactants) of uniqueness of this solution and of existence of non-constant solutions. In particular, it is shown that no non-constant solution is possible provided that the diffusivity of one reactant is high enough. Conditions on the existence of such solution are given in terms of eigenvalues of the Laplace operator with boundary conditions in the domain.
scientific article; zbMATH DE number 5912743