论文标题
带有条纹场的MEMS模型的径向常规和破裂溶液
Radial regular and rupture solutions for a MEMS model with fringing field
论文作者
论文摘要
我们研究了问题\ [\ begin {case} \ displaystyle-ΔU= \ frac {λ+δ| \ nabla u |^2} {1 -u}，\; u> 0＆\ textrm {in} \ b，\\ u = 0＆\ textrm {on} \ \ partial b，\ end b，end end {cases} \]，这与微电动机电系统（MEMS）的研究有关。在这里，$ b \ subset \ mathbb {r}^n $ $（n \ geq 2）$表示打开的单位球，$λ，δ> 0 $是实数。在这项工作中考虑了两类解决方案：（i）{\ it常规解决方案}，满足$ 0 <u <1 $ in $ b $和（ii）{\ it rupture solutture soluttions}，它满足$ u（0）= 1 $，从而使方程式在原点上使方程式单数。还讨论了有关参数$λ> 0 $的分叉。
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.
