发表机构
Brown University; The Ohio State University; Duke University（布朗大学; 俄亥俄州立大学; 杜克大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究有限电导率夹杂物间不完美粘接界面导致的场集中，揭示梯度爆破依赖于粘接参数γ，并确定阈值、最优爆破速率及临界值处的对数爆破现象。
AI 中文摘要
我们研究两个紧密间隔的夹杂物之间的场集中现象，这些夹杂物具有低电导率类型的不完美粘接界面。假设夹杂物具有有限电导率。该问题由一组椭圆方程与Robin型边界条件耦合控制。虽然已知具有理想界面的有限电导率夹杂物产生有界梯度，但在本文中我们表明，对于不完美粘接界面，当粘接参数γ较大时，随着ε（两个夹杂物之间的距离）趋于零，解的梯度可能爆破，而当粘接参数γ较小时，梯度一致有界且不依赖于ε。此外，我们在某些对称性假设下确定了γ的阈值和最优爆破速率。与夹杂物为完美导体的情况相比，我们在γ的临界值处发现了一种新的对数爆破现象。
英文摘要
We study the field concentration phenomenon between two closely spaced inclusions with imperfect bonding interfaces of low conductivity type. The inclusions are assumed to have finite conductivities. The problem is governed by a system of elliptic equations coupled with Robin-type boundary conditions. While it is known that finite-conductivity inclusions with ideal interfaces yield bounded gradients, in this paper we show that with imperfect bonding interfaces, the gradient of the solution may blow up as $\varepsilon$ (the distance between two inclusions) tends to zero when the bonding parameter $γ$ is large, while it is uniformly bounded independently of $\varepsilon$ when the bonding parameter $γ$ is small. Moreover, we identify the threshold of $γ$ and the optimal blow-up rates under certain symmetry assumptions. Compared to the case when the inclusions are perfect conductors, we find a novel logarithmic blow-up phenomenon at the critical value of $γ$.
Comments44 pages
