Global existence result for phase transformations with heat transfer in shape memory alloys
- Paoli, Laetitia
- Petrov, Adrien
2010 Mathematics Subject Classification
- 35K55 74C05 74C10
- Existence result, generalized standard materials, heat equation, enthalpy transformation, maximal monotone operators, doubly nonlinear equations, shape-memory alloys
We consider three-dimensional models for rate-independent processes describing materials undergoing phase transformations with heat transfer. The problem is formulated within the framework of generalized standard solids by the coupling of the momentum equilibrium equation and the flow rule with the heat transfer equation. Under appropriate regularity assumptions on the initial data, we prove the existence a global solution for this thermodynamically consistent system, by using a fixed-point argument combined with global energy estimates.