Cahn-Hilliard model with Schl\"ogl reactions: interplay of equilibrium and non-equilibrium phase transitions. I. Travelling wave solutions

Abstract

The present work is devoted to the modelling which is based on the modified Cahn-Hilliard equation, the interplay of equilibrium and non-equilibrium phase transitions. The non-equilibrium phase transitions are modelled by the Schl\"ogl reactions systems. We consider the advancing fronts which combine these both transitions. The traveling wave solutions are obtained; the conditions of their existence and dependence on the parameters of the models are studied in detail. The possibility of the existance of non-equilibrated phase is discussed.