论文标题
孔素脉冲溶液对大型可变的半线性双曲系统的反射
Reflection of conormal pulse solutions to large variable-coefficient semilinear hyperbolic systems
论文作者
论文摘要
我们提供了一个非线性几何光学光学扩展的严格依据，用于在空间尺寸中反映\ emph {pulses} $ n> 1 $。这些脉冲是作为可变系数半线性一阶双曲系统的解决方案而产生的。该理由适用于$ n \ times n $系统，其$ n $相互作用的脉冲取决于可能是非线性的阶段。 \ emph {cooherence}在许多较早作品中做出的假设被删除。我们考虑了从脉冲边界数据产生传入的脉冲的问题，以及单个传出脉冲反映可能弯曲边界以产生许多传入的脉冲的问题。尽管我们在这里专注于边界问题，但很明显，对于$ n \ times n $ systems的cauchy问题，通过相似的方法在自由空间中得以实现。
We provide a rigorous justication of nonlinear geometric optics expansions for reflecting \emph{pulses} in space dimensions $n>1$. The pulses arise as solutions to variable coefficient semilinear first-order hyperbolic systems. The justification applies to $N\times N$ systems with $N$ interacting pulses which depend on phases that may be nonlinear. The \emph{coherence} assumption made in a number of earlier works is dropped. We consider problems in which incoming pulses are generated from pulse boundary data as well as problems in which a single outgoing pulse reflects off a possibly curved boundary to produce a number of incoming pulses. Although we focus here on boundary problems, it is clear that similar results hold by similar methods for the Cauchy problem for $N\times N$ systems in free space.
