椭圆壳中敏感奇异扰动的严格和启发式处理
Rigorous and heuristic treatment of sensitive singular perturbations arising in elliptic shells
摘要：
我们考虑椭圆型方程组依赖于参数的奇异扰动？这样，对于？= 0时，边界条件不适用于方程（它们不满足Shapiro-Lopatinskii条件）。极限只在非常抽象的空间，分布理论，涉及复杂的？阳离子和非局部现象。在薄壳理论中，当中间面为椭圆形，壳体在边界的一部分上固定而在其余部分上自由时，出现这种系统。我们使用启发式推理应用一些简化，允许减少原来的问题在一个域的另一个问题在其边界上。这项工作的新颖之处在于，我们认为系统的偏微分方程，而在我们以前的工作中，我们正在处理单一的方程。
英文摘要：
We consider singular perturbations of elliptic systems depending on a parameter ? such that, for ? = 0 the boundary conditions are not adapted to the equation (they do not satisfy the Shapiro - Lopatinskii condition). The limit holds only in very abstract spaces out of distribu- tion theory involving complexi?cation and non-local phenomena. This system appears in the thin shell theory when the middle surface is el- liptic and the shell is fixed on a part of the boundary and free on the rest. We use a heuristic reasoning applying some simplifications which allow to reduce the original problem in a domain to another problem on its boundary. The novelty of this work is that we consider systems of partial differential equations while in our previous work we were dealing with single equations.
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