Fedotov S
Department of Mathematics, UMIST, Manchester M60 1QD, United Kingdom.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 May;59(5 Pt A):5040-4. doi: 10.1103/physreve.59.5040.
The problem of wave-front propagation for the n-dimensional reaction-diffusion system involving Kolmogorov-Petrovskii-Piskunov kinetics and the diffusion transport with a finite velocity has been considered. By using a scaling procedure we have given an asymptotic derivation of the equation governing the evolution of a reaction front in the long-time large-distance limit. It has been found that this equation is identical in form to the relativistic Hamilton-Jacobi equation. In the case of a constant value of chemical rate function we have derived exact formulas for the position of reaction front and the speed of propagation by using relativistic mechanics techniques.
研究了涉及柯尔莫哥洛夫-彼得罗夫斯基-皮斯库诺夫动力学的n维反应扩散系统以及具有有限速度的扩散输运中的波前传播问题。通过使用一种标度程序，我们给出了在长时间大距离极限下控制反应前沿演化方程的渐近推导。已经发现该方程在形式上与相对论哈密顿-雅可比方程相同。在化学速率函数为常数的情况下，我们使用相对论力学技术推导了反应前沿位置和传播速度的精确公式。
