Metastable structure of the Cahn-Hilliard equation
The Cahn-Hilliard equation at a segment with the boundary condition is considered. For the construction and analysis of stationary solutions of slowly varying solutions we use the Galerkin approximations of the average dimensions (30 - 40). It is found that in two-parameter families of differential equations there are realized saddle-node bifurcations, to the continuous branches of stationary solutions of which, the continuous branches of approximate stationary solutions of the transition layer type with two and three transition points correspond. These solutions generate metastable structures (slowly varying solutions). The analysis conducted suggests that the use of the Galerkin method in the problem of metastable structures leads to qualitatively and quantitatively correct results.