Analysis of a system related to a model for phase transitions in dissipative isochoric thermoviscoelastic materials

作者：Assuncao Welington Vieira; Boldrini Jose Luiz^*

来源：Mathematical Methods in the Applied Sciences, 2017, 40(10): 3504-3527.

DOI：10.1002/mma.4241

• nonlinear PDE system
• changing type PDE system
• global existence of solutions
• uniqueness of solutions
• phase transitions
• thermoviscoelastic material
• isochoric material

We analyze a highly nonlinear system of partial differential equations related to a model solidification and/or melting of thermoviscoelastic isochoric materials with the possibility of motion of the material during the process. This system consists of an internal energy balance equation governing the evolution of temperature, coupled with an evolution equation for a phase field whose values describe the state of material and a balance equation for the linear moments governing the material displacements. For this system, under suitable dissipation conditions, we prove global existence and uniqueness of weak solutions.

• 出版日期2017-7-15