Title: Continua with non-local constitutive laws: exploitation of entropy inequality Show Chinese title

Title: 具有非局部本构定律的连续体：熵不等式的应用

Abstract: In this paper, we consider a system of balance laws sufficiently general to contain the equations describing the thermomechanics of a one-dimensional continuum; this system involves some constitutive functions depending on the elements of the so called state space assumed to contain the spatial gradients of some of the unknown fields. The compatibility of the constitutive equations with an entropy-like principle is considered via an extended Liu procedure by using as constraints both the balance equations and some of their gradient extensions. This procedure is then applied to the equations of a fluid whose description involves an internal variable and first order non-local constitutive relations, and to a Korteweg fluid with second order non-localities. In both cases, the restrictions placed by an entropy inequality are solved, and an explicit solution for the constitutive equations is provided. Show Chinese abstract

Abstract: 在本文中，我们考虑一个足够一般的平衡律系统，以包含描述一维连续体热力学的方程；该系统涉及一些本构函数，这些函数依赖于所谓的状态空间中的元素，该状态空间包含某些未知场的空间梯度。 通过使用扩展的Liu过程，通过将平衡方程及其某些梯度扩展作为约束条件，来考虑本构方程与类似熵原理的相容性。 然后，该过程被应用于涉及内部变量和一阶非局部本构关系的流体方程，以及具有二阶非局部性的Korteweg流体方程。 在这两种情况下，由熵不等式施加的限制都被解决，并提供了本构方程的显式解。