带边缘场的MEMS模型的径向正则解与破裂解
Radial regular and rupture solutions for a MEMS model with fringing field
AI总结：
该研究针对带边缘场的MEMS相关偏微分方程，分析N维开单位球内的径向正则解与破裂解两类解的性质，并探讨了关于参数λ的分岔问题。
摘要：
我们研究如下问题的径向解，该问题与微机电系统（Micro-Electromechanical Systems, MEMS）的研究相关：方程为-ΔU=(λ+δ|∇U|²)/(1-U)，在区域B内U>0，在边界∂B上U=0。其中B⊂ℝᴺ（N≥2）表示开单位球，λ、δ>0为实数。本文考虑两类解：（i）正则解，满足在B内0<U<1；（ii）破裂解，满足U(0)=1，因此方程在原点处奇异。本文还讨论了关于参数λ>0的分岔现象。
英文摘要：
We investigate radial solutions for the problem \[ \begin{cases} \displaystyle -ΔU=\frac{λ+δ|\nabla U|^2}{1-U},\; U>0 & \textrm{in}\ B,\\ U=0 & \textrm{on}\ \partial B, \end{cases} \] which is related to the study of Micro-Electromechanical Systems (MEMS). Here, $B\subset \mathbb{R}^N$ $(N\geq 2)$ denotes the open unit ball and $λ, δ>0$ are real numbers. Two classes of solutions are considered in this work: (i) {\it regular solutions}, which satisfy $0<U<1$ in $B$ and (ii) {\it rupture solutions} which satisfy $U(0)=1$, and thus make the equation singular at the origin. Bifurcation with respect to parameter $λ>0$ is also discussed.
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。
