[Stability of spatially nonuniform states of diffuse systems]

The problem of stability of inhomogeneous stationary states in kinetic systems with nonlinear local dynamics and diffusion is studied. Stability criterion applicable in the case of one rate equation or two coupled rate equations with the diffusion term presented at one of them is formulated in the integral form. It is made the conclusion on the absence of stable inhomogeneous stationary states in the unicomponent system with zero fluxes at the boundaries and the case of periodic boundary conditions. In the case of non-zero fluxes at the boundaries the condition of stability of exfoliated stationary structures in the systems with bistable local dynamics is given.