Asymptotic behaviour for a phase-field model with hysteresis in one-dimensional thermo-visco-plasticity.
The author considers a system of partial differential equations in one space dimension, describing the balances of momentum and internal energy coupled with a differential phase dynamics equation, with the intention to characterize the long time evolution of a thermo-visco-elasto-plastic wire under the influence of a solid-solid phase transition in the material. Hysteresis effects in both the plastic constitutive law and in the phase transition are taken into account. In addition to a generalization of existence, uniqueness, and thermodynamic consistency results obtained in \textit{P.\ Krejčí, J.\ Sprekels} and \textit{U.\ Stefanelli} [SIAM J.\ Math.\ Anal.\ 34, 409-434 (2002; Zbl 1034.34053)], a careful estimation technique based on energy dissipation properties of hysteresis operators is used here to prove under weaker assumptions new results on asymptotic stability as time tends to infinity.
scientific article; zbMATH DE number 5074726