一个宇宙弦方程的爆破分析
Blow up analysis for a cosmic strings equation
摘要：
本文研究了一类含指数非线性项的平面半线性椭圆型方程解的爆破分析。这样的解决方案描述宇宙弦，我们展示了他们的爆破行为是如何由新的和令人惊讶的现象。例如，在某些情况下，解的爆破轮廓被描述为微分问题，该微分问题在具有圆锥奇点的黎曼球的均匀化的上下文中具有几何意义。
英文摘要：
In this paper we develop a blow up analysis for solutions of a planar semilinear elliptic equation involving exponential nonlinearities. Such solutions describe cosmic strings, and we show how their blow up behaviour is characterised by new and surprising phenomena. For example in some cases, the blow up profile of the solution is described in terms of a differential problem that bares a geometrical meaning in the context of the uniformization of the Riemann sphere with conical singularities.
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