具有强吸收的慢扩散方程反向界面自相似解的分支
Bifurcations of self-similar solutions for reversing interfaces in the slow diffusion equation with strong absorption
摘要：
研究了具有强吸收的慢扩散方程在反向界面上的自相似解的分支。自相似解从固定界面的时间无关解中分支出来。我们表明，这样的分歧发生在分歧点，在那里的合流超几何函数满足Kummer的微分方程被截断为一个有限的多项式。利用双尺度渐近方法得到了自相似反转界面在分岔点附近的渐近依赖性。渐近结果与数值计算结果吻合得很好。
英文摘要：
Bifurcations of self-similar solutions for reversing interfaces are studied in the slow diffusion equation with strong absorption. The self-similar solutions bifurcate from the time-independent solutions for standing interfaces. We show that such bifurcations occur at the bifurcation points, at which the confluent hypergeometric functions satisfying Kummer's differential equation is truncated into a finite polynomial. A two-scale asymptotic method is employed to obtain the asymptotic dependencies of the self-similar reversing interfaces near the bifurcation points. The asymptotic results are shown to be in excellent agreement with numerical computations.
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