论文标题
具有非Convex储存能量的粘弹性开尔文 - Voigt模型的存在和独特性
Existence and uniqueness for a viscoelastic Kelvin-Voigt model with nonconvex stored energy
论文作者
论文摘要
我们考虑开尔文 - voigt类型的非线性粘弹性材料，具有满足Andrews-ball条件的储存能量，从而在紧凑的集合中允许非凸度。在$ h^1 $中的变形梯度的存在较弱的解决方案是为了任何超质量增长的能量而建立的。在两个空间维度中，弱解决方案在此类中显然是唯一的。在两个维度和三个维度中的弱解决方案以及在二维中平滑初始数据的全球规律性的保护均在对存储能量生长的额外限制下建立。
We consider nonlinear viscoelastic materials of Kelvin-Voigt type with stored energies satisfying an Andrews-Ball condition, allowing for non convexity in a compact set. Existence of weak solutions with deformation gradients in $H^1$ is established for energies of any superquadratic growth. In two space dimensions, weak solutions notably turn out to be unique in this class. Conservation of energy for weak solutions in two and three dimensions, as well as global regularity for smooth initial data in two dimensions are established under additional mild restrictions on the growth of the stored energy.
