Mathematical Sciences: Systems of Evolution Equations in Thermomechanical Processes

这项研究计划调查的竞争 摩擦等耗散机制与 材料响应的非线性失稳作用。 相应的非线性演化（偏微分） 方程表现出双曲和抛物的特点。 他们对物质的定性行为的分析 系统提出了新的和困难的数学问题。 该研究计划的具体成果预计将 提供对剪切带等物理问题的洞察力 应变率相关材料的形成和运动 具有衰减记忆的粘弹性材料。

This research program investigates the competition between dissipative mechanisms such as frictions and the destabilizing action of nonlinearity of the material response. The corresponding nonlinear evolution (partial differential) equations exhibit both hyperbolic and parabolic characters. Their analysis for the qualitative behavior of the physical system poses new and difficult mathematical problems. Specific results from the research program are expected to provide insight to physical problems such as shear band formation for strain-rate dependent materials and the motion of viscoelastic materials with fading memory.