标题： 热粘弹性中耦合粘塑性-损伤模型的存在性结果 显示英文标题

标题： Existence results for a coupled viscoplastic-damage model in thermoviscoelasticity

摘要： 在本文中，我们研究了一个将粘塑性与损伤耦合的热粘弹性模型。相关的PDE系统包括位移变量的小应变下的动量平衡方程，包含粘性和惯性项，塑料和损伤流动规则，以及热方程。它具有强烈的非线性特征，特别是热方程和损伤流动规则的右边有二次项，必须仔细处理。我们为相关初边值问题提出了两种弱解概念，即“熵”解和“弱能量”解。相应地，我们通过精心设计的时间离散化方案取极限，证明了两个存在性结果。最后，在给定温度分布的情况下，并在一种高度简化的条件下，我们提供了连续依赖结果，从而得到弱能量解的唯一性。 显示英文摘要

摘要： In this paper we address a model coupling viscoplasticity with damage in thermoviscoelasticity. The associated PDE system consists of the momentum balance with viscosity and inertia for the displacement variable, at small strains, of the plastic and damage flow rules, and of the heat equation. It has a strongly nonlinear character and in particular features quadratic terms on the right-hand side of the heat equation and of the damage flow rule, which have to be handled carefully. We propose two weak solution concepts for the related initial-boundary value problem, namely `entropic' and `weak energy' solutions. Accordingly, we prove two existence results by passing to the limit in a carefully devised time discretization scheme. Finally, in the case of a prescribed temperature profile, and under a strongly simplifying condition, we provide a continuous dependence result, yielding uniqueness of weak energy solutions.