AN INVITATION TO NONLOCAL MODELING, ANALYSIS AND COMPUTATION
AN INVITATION TO NONLOCAL MODELING, ANALYSIS AND COMPUTATION
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DOI：
10.1142/9789813272880_0191
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发表时间：
2019-05
期刊：
影响因子：
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通讯作者：
Q. Du
中科院分区：
文献类型：
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作者：
Q. Du
本次讲座邀请进一步研究非局部模型，它们的数学，计算和应用。我们的样本我们最近的尝试，在发展一个系统的数学框架，非局部模型，包括基本要素的非局部向量微积分，适定性的非局部变分问题，耦合到本地模型，收敛性和兼容性的数值逼近，以及应用到非局部力学和扩散。我们还与传统模型和其他相关数学学科建立了联系。
This lecture serves as an invitation to further studies on nonlocal models, their mathematics, computation, and applications. We sample our recent attempts in the development of a systematic mathematical framework for nonlocal models, including basic elements of nonlocal vector calculus, well-posedness of nonlocal variational problems, coupling to local models, convergence and compatibility of numerical approximations, and applications to nonlocal mechanics and diffusion. We also draw connections with traditional models and other relevant mathematical subjects.