论文标题
关于圆柱和球形kDV爆炸方程的周期性边界解决方案
On periodic boundary solutions for cylindrical and spherical KdV-Burgers equations
论文作者
论文摘要
对于圆柱和球形波的KDV-燃烧方程，研究了从边界处的周期性扰动下从平衡开始的常规轮廓的发展。该方程式描述了一种既具有耗散又具有分散性的介质。为了使色散和散布的适当组合，渐近轮廓看起来像是一条周期性的冲击阵列链，幅度降低（锯齿波）。在此类轮廓的开发之前是恒定高度和相等速度的头部冲击，这取决于空间维度以及边界条件的积分特征。发现对这种头部冲击的明确渐近线。
For the KdV-Burgers equations for cylindrical and spherical waves the development of a regular profile starting from an equilibrium under a periodic perturbation at the boundary is studied. The equation describes a medium which is both dissipative and dispersive. For an appropriate combination of dispersion and dissipation the asymptotic profile looks like a periodical chain of shock fronts with a decreasing amplitude (sawtooth waves). The development of such a profile is preceded by a head shock of a constant height and equal velocity which depends on spatial dimension as well as on integral characteristics of boundary condition; an explicit asymptotic for this head shock is found.
