波映射中的参数共振
Parametric Resonance in Wave Maps
摘要：
本文研究了从具有周期时间度量的Lorentz流形到单参数黎曼流形的Riemann流形的波映射。该族包含作为特殊情况的庞加莱上半平面模型。我们对这种映射的兴趣是由宇宙学中出现的某些特殊类型的罗伯逊-沃克时空激发的。我们表明，小周期性的时间微扰的闵可夫斯基度规产生参数共振现象。证明了在常值解邻域内的整体时间可解性不是波映射的稳定性质。
英文摘要：
In this note we concern with the wave maps from the Lorentzian manifold with the periodic in time metric into the Riemannian manifold, which belongs to the one-parameter family of Riemannian manifolds. That family contains as a special case the Poincare upper half-plane model. Our interest to such maps is motivated with some particular type of the Robertson-Walker spacetime arising in the cosmology. We show that small periodic in time perturbation of the Minkowski metric generates parametric resonance phenomenon. We prove that, the global in time solvability in the neighborhood of constant solutions is not a stable property of the wave maps.
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