粘弹性材料损伤系统的存在性与弱-强唯一性
Existence and weak-strong uniqueness for damage systems in viscoelasticity
AI总结：
本文针对粘弹性材料损伤的偏微分方程系统，证明了弱解的全局存在性和强解的局部存在性，并利用相对能量不等式建立了强解在弱解类中的唯一性。
摘要：
本文研究了一个描述粘弹性材料损伤的偏微分方程系统解的存在性及其弱-强唯一性。事实上，我们讨论了两种解的概念：弱解和强解。对于弱解，我们得到了全局时间存在性结果，但系统的高度非线性特征使我们无法证明其唯一性。对于强解，我们证明了局部时间存在性。随后，我们证明强解只要存在，就在弱解类中是唯一的。这一弱-强唯一性结论通过一个合适的相对能量不等式加以证明。
英文摘要：
In this paper we investigate the existence of solutions and their weak-strong uniqueness property for a PDE system modelling damage in viscoelastic materials. In fact, we address two solution concepts, weak and strong solutions. For the former, we obtain a global-in-time existence result, but the highly nonlinear character of the system prevents us from proving their uniqueness. For the latter, we prove local-in-time existence. Then, we show that the strong solution, as long as it exists, is unique in the class of weak solutions. This weak-strong uniqueness statement is proved by means of a suitable relative energy inequality.
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。
