Generic properties of equilibria of reaction-diffusion equations with variable diffusion
Carlos Raphael Rocha · Proceedings of the Royal Society of Edinburgh Section A Mathematics · 1985
Synopsis It is shown that, generically, scalar one-dimensional parabolic equations ut = (a2(x)ux)x + f(u), x ∈ [0, 1], with Neumann boundary conditions, have all the equilibrium solutions hyperbolic. Moreover, the bifurcations of these equilibria are generically of the saddle-node type.