关于圆柱和球面KdV-Burgers方程的周期边界解
On periodic boundary solutions for cylindrical and spherical KdV-Burgers equations
摘要：
对于圆柱波和球面波的KdV-Burgers方程，研究了在边界处周期扰动下从平衡开始的规则轮廓的发展。该方程描述了一种既耗散又色散的介质。对于色散和耗散的适当组合，渐近剖面看起来像一个振幅逐渐减小的周期性激波阵面链（激波）。这样一个配置文件的发展之前，由一个恒定的高度和速度相等的头部冲击，这取决于空间尺寸以及边界条件的积分特性;这个头部冲击的一个明确的渐近发现。
英文摘要：
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.
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