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The present work is devoted to the modelling which is based on the modifiedCahn-Hilliard equation, the interplay of equilibrium and non-equilibrium phasetransitions. The non-equilibrium phase transitions are modelled by theSchl\"ogl reactions systems. We consider the advancing fronts which combinethese both transitions. The traveling wave solutions are obtained; theconditions of their existence and dependence on the parameters of the modelsare studied in detail. The possibility of the existance of non-equilibratedphase is discussed.

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