具有排斥非线性项的传输问题解的整体存在性和因果性
Global existence and causality for a transmission problem with a repulsive nonlinearity
摘要：
众所周知，具有紧支撑初始条件和零初速度的经典线性波动方程的解也在依赖于时间的集合中紧支撑：解在时间t的支撑与初始给定条件的支撑有因果关系。Reed和Simon证明了对于一个具有（非线性）右手边$- λu^3$的实值Klein-Gordon方程，因果关系仍然成立。对于一维Klein-Gordon问题，我们证明了同样的性质，但具有传输和更一般的排斥性非线性右手边$F$。利用$F$的排斥性证明了解的整体存在性.在$F(u) = - λu^3$的特殊情况下，问题是一个量子粒子的物理模型，该模型受到自相互作用和势阶的影响。
英文摘要：
It is well-known that the solution of the classical linear wave equation with compactly supported initial condition and vanishing initial velocity is also compactly supported in a set depending on time : the support of the solution at time t is causally related to that of the initially given condition. Reed and Simon have shown that for a real-valued Klein-Gordon equation with (nonlinear) right-hand side $- λu^3$, causality still holds. We show the same property for a one-dimensional Klein-Gordon problem but with transmission and with a more general repulsive nonlinear right-hand side $F$. We also prove the global existence of a solution using the repulsiveness of $F$. In the particular case $F(u) = - λu^3$, the problem is a physical model for a quantum particle submitted to self-interaction and to a potential step.
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