Stability and other considerations for a nonlinear diffusion system

A nonlinear double diffusive system is the subject of this article: we consider two simultaneous p.d.e.'s in two dependent variables, first order in time and second order in the spatial variables. Dirichlet boundary conditions, independent of time, are assumed. The principal concern of the article is the stability of the steady states together with the convergence of the unsteady states thereto. Novel Liapunov functionals are used to this end. Both linear and nonlinear stability are discussed together with some aspects of (linear) instability. Prior to these considerations, some relevant remarks are made concerning uniqueness and nonuniqueness of the steady state