粘性双场梯度损伤模型的分析Ⅰ：存在唯一性

IF 0.7 3区数学 Q2 MATHEMATICS

Zeitschrift fur Analysis und ihre Anwendungen Pub Date : 2019-07-15 DOI:10.4171/ZAA/1637

C. Meyer, L. Susu

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引用次数: 9

摘要

本文讨论了一个粘性损伤模型，该模型包括两个损伤变量，一个是局部损伤变量，另一个是非局部损伤变量。在一定的正则性条件下，证明了线性弹性方程解的存在性和唯一性，前提是惩罚参数选择得足够大。此外，还研究了唯一解的正则性，特别是关于时间的可微性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Analysis of a Viscous Two-Field Gradient Damage Model I: Existence and Uniqueness

The paper deals with a viscous damage model including two damage variables, a local and a non-local one, which are coupled through a penalty term in the free energy functional. Under certain regularity conditions for linear elasticity equations, existence and uniqueness of the solution is proven, provided that the penalization parameter is chosen sufficiently large. Moreover, the regularity of the unique solution is investigated, in particular the differentiability w.r.t. time.

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来源期刊

Zeitschrift fur Analysis und ihre Anwendungen 数学-数学

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Analysis and its Applications aims at disseminating theoretical knowledge in the field of analysis and, at the same time, cultivating and extending its applications. To this end, it publishes research articles on differential equations and variational problems, functional analysis and operator theory together with their theoretical foundations and their applications – within mathematics, physics and other disciplines of the exact sciences.