论文标题
自相似溶液在多项式子片段分布的片段化方程式的稳定性
Stability of selfsimilar solutions to the fragmentation equation with polynomial daughter fragments distribution
论文作者
论文摘要
我们研究了具有幂律碎片率和多项式碎片分布函数$ p（s）$的碎裂方程。分析了相应的自动固定解决方案，并呈指数衰减的渐近行为和$ c^{\ infty} $定期。自我相似解决方案的稳定性（在呈指数衰减的光滑下），及时呈尖锐的衰减率，以及$ c^{\ infty} $ $ t> 0 $的规律解决方案。结果基于广义拉瓜多项式的显式扩展和此类扩展的分析。对于在无限稳定性下具有幂律衰减的扰动。最后，我们考虑真正的分析$ P（S）$。
We study fragmentation equations with power-law fragmentation rates and polynomial daughter fragments distribution function $p(s)$. The corresponding selfsimillar solutions are analysed and their exponentially decaying asymptotic behaviour and $C^{\infty }$ regularity deduced. Stability of selfsimilar solutions (under smooth exponentially decaying perturbations), with sharp exponential decay rates in time are proved, as well as $C^{\infty }$ regularity of solutions for $t>0$. The results are based on explicit expansion in terms of generalized Laguerre polynomials and the analysis of such expansions. For perturbations with power-law decay at infinity stability is also proved. Finally, we consider real analytic $p(s)$.
