Phase transitions and partial differential equations of mixed types

点击翻译按钮获取中文摘要

Phase transitions are very common phenomena arising in thermodynamics. Two important type of models are the compressible van der Waals fluid flow and the model of viscoelastic material dynamics. In the van der Waals flow, due to the variety of the absolute temperature and the non-monotony of the pressure function, the flow usually exhibits phase transitions between water, vapor and mixtures of water and vapor. While in the model of viscoelastical material dynamics, due to the change of the non-monotonic stress function, the system behaves as three phases-soft material, hard material and the mixture of soft and hard material.