Abstract

Mathematical models of the dynamics of elastoplastic, granular, and porous media are reduced to variational inequalities for hyperbolic differential operators that are thermodynamically consistent in the sense of Godunov. On this basis, the concept of weak solutions with dissipative shock waves is introduced and a priori estimates of smooth solutions in characteristic conoids of operators are constructed, which suggest the well-posedness of the formulation of the Cauchy problem and boundary value problems with dissipative boundary conditions. Additionally, efficient shock-capturing methods adapted to solution discontinuities are designed.

中文翻译：

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弹塑性，粒状和多孔材料理论中的热力学一致性和数学上的正确性

摘要

弹塑性，粒状和多孔介质动力学的数学模型被简化为双曲型微分算子的变分不等式，这在Godunov的意义上是热力学一致的。在此基础上，引入了具有耗散冲击波的弱解的概念，并构造了算子特征圆锥中光滑解的先验估计，这说明了具有耗散边界的柯西问题和边值问题的拟定性。条件。此外，还设计了适用于解决方案不连续性的有效防震方法。