拉格朗日和欧拉坐标系下具有多凸熵的应力松弛模型
Stress relaxation models with polyconvex entropy in Lagrangean and Eulerian coordinates
摘要：
将多凸弹性动力学方程嵌入增广对称双曲方程组，结合相对熵方法，为近似解提供了一个鲁棒稳定性框架。我们在这里设计一个模型的应力松弛激发的格式的扩大过程，正式近似方程的多凸弹性动力学。该模型被赋予一个熵函数，它不是凸的，而是多凸型的。利用相对熵，我们证明了多凸弹性动力学应力松弛模型在光滑区域的稳定性估计和收敛性。作为一个应用程序，我们表明，模型的压力松弛的真实气体在欧拉坐标适合到建议的框架。
英文摘要：
The embedding of the equations of polyconvex elastodynamics to an augmented symmetric hyperbolic system provides in conjunction with the relative entropy method a robust stability framework for approximate solutions. We devise here a model of stress relaxation motivated by the format of the enlargement process which formally approximates the equations of polyconvex elastodynamics. The model is endowed with an entropy function which is not convex but rather of polyconvex type. Using the relative entropy we prove a stability estimate and convergence of the stress relaxation model to polyconvex elastodynamics in the smooth regime. As an application, we show that models of pressure relaxation for real gases in Eulerian coordinates fit into the proposed framework.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
