Abstract
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) $.
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