POSITIVITY OF TEMPERATURE IN THE GENERAL FREMOND MODEL FOR SHAPE-MEMORY ALLOYS

In this paper, we consider a model introduced by M. Fremond to describ e the martensitic phase transitions in shape memory alloys. In the der ivation of his model, M. Fremond made the (physically reasonable) assu mption that the state variable representing the absolute temperature i s always positive. Although various results concerning existence and u niqueness of solutions to certain simplified versions of the governing field equations have been established in the past, it has been an ope n problem if the positivity of temperature can be recovered from the m odel. In our contribution, we give a rigorous proof that, under rather weak assumptions on the data of the system, any sufficiently smooth s olution of the governing field equations has indeed the property that the absolute temperature variable attains positive values almost every where. The method of proof applies to all the simplified versions of t he field equations that have been studied in the literature.