In this paper, we study a system of partial differential equations defined in a moving domain. This system is defined by a heat equation and a diffusion equation for a concentration of non-Fickian type whose diffusion coefficient depends on the temperature, completed with suitable initial and boundary conditions. The non-Fickian mass flux is established considering the viscoelastic properties of the medium where the strain depends on the temperature and on the concentration. The initial boundary value problem (IBVP) analyzed can be used to describe the drying of viscoelastic materials where the internal structure offers a resistance to the movement of the moisture molecules and a consequent delay in the moisture removal. Due to heat transference into the materials and moisture removal, shrinkage of the medium occurs. The stability of the IBVP defined in a moving domain is analyzed and its qualitative behavior is numerically studied.

中文翻译：

---

干燥粘弹性材料：非菲克式方法

在本文中，我们研究了在移动域中定义的偏微分方程组。该系统由热方程和扩散方程式定义，该方程式的扩散系数取决于温度，且扩散方程取决于温度，且扩散条件取决于初始条件和边界条件。考虑到介质的粘弹性质（其中应变取决于温度和浓度），可以建立非菲克质量通量。分析的初始边界值问题（IBVP）可用于描述粘弹性材料的干燥，其内部结构可抵抗水分分子的运动并因此延迟水分去除。由于热量传递到材料中并除去水分，导致介质收缩。