THE PENROSE-FIFE-TYPE EQUATIONS - COUNTING THE ONE-DIMENSIONAL STATIONARY SOLUTIONS

A method for counting the solutions for Penrose-Fife-type phase held e quations is derived. The method used is similar to that developed rece ntly for obtaining a precise count for the number of solutions for the Cahn-Hilliard equation [9], and is based on the derivation of an exte nded system of Picard-Fuchs equations as well as on estimates obtained in [11]. The Penrose-Fife-type phase held equations represent a therm odynamically consistent model for phase separation of a conserved orde r parameter (typically concentration) in binary systems in which laten t heat effects are important in the phase separation process.