Stability of stationary solutions of extended reaction-diffusion- convection equations on a finite segment (Q1175146)

The linear stability of the stationary solutions of the problem \(f(u,u_ x,u_{xx},u_ t)=0\) in \(0<x<\ell\), \(t>0\), \(B_ i(u,u_ x)=0\) at \(x=i\ell\), for \(i=0,1,\;0<\ell<\infty\), is under consideration. The main result contains conditions for which the sign of the largest eigenvalue of the linearised problem is established. These conditions are formulated in terms of so-called types of linearised problem boundary conditions with regard to the number of critical points of the stationary solutions.