论文标题
对MEMS半线性波方程的淬火
Quenching for a semi-linear wave equation for MEMS
论文作者
论文摘要
我们考虑为具有负功率非线性的半线性波方程解的有限时间淬火奇异性的形成，对微电力机械系统（MEMS）的模型也可以。对于径向初始数据，我们正式获得了一系列淬灭自相似溶液的序列。同样是正式的渐近分析，这是对PDE的解决方案，它是径向对称的，并严格地单调地增加了与原点的距离，就像显式在空间独立的溶液一样。后者的分析和数值实验表明了对奇异行为的详细猜想。
We consider the formation of finite-time quenching singularities for solutions of semi-linear wave equations with negative power nonlinearities, as can model micro-electro-mechanical systems (MEMS). For radial initial data we obtain, formally, the existence of a sequence of quenching self-similar solutions. Also from formal asymptotic analysis, a solution to the PDE which is radially symmetric and increases strictly monotonically with distance from the origin quenches at the origin like an explicit spatially independent solution. The latter analysis and numerical experiments suggest a detailed conjecture for the singular behaviour.
