On the characteristic initial value problem for nonlinear symmetric hyperbolic systems, including Einstein equations
On the characteristic initial value problem for nonlinear symmetric hyperbolic systems, including Einstein equations
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DOI：
10.4064/dm732-7-2015
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发表时间：
2014-06
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影响因子：
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通讯作者：
Aurore Cabet;P. T. Chru'sciel;R. Wafo
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文献类型：
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作者：
Aurore Cabet;P. T. Chru'sciel;R. Wafo
考虑一类对称双曲组的特征初值问题，其初值给定在两个光滑的零相交的特征曲面上。我们证明了在初始曲面的未来邻域上解的存在性。一般结果适用于一般的半线性波动方程，以及有或无源的爱因斯坦方程及其保角变分。
We consider a characteristic initial value problem for a class of symmetric hyperbolic systems with initial data given on two smooth null intersecting characteristic surfaces. We prove existence of solutions on a future neighborhood of the initial surfaces. The general result is applied to general semilinear wave equations, as well as the Einstein equations with or without sources, and conformal variations thereof.