Optimal Bounds for Self-Similar Solutions to Coagulation Equations with Product Kernel |
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| Authors: | B Niethammer J J L Velázquez |
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| Institution: | 1. Mathematical Institute , University of Oxford , Oxford, England niethammer@maths.ox.ac.uk;3. ICMAT (CSIC-UAM-UC3?M-UCM) , Madrid, Spain |
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| Abstract: | We consider mass-conserving self-similar solutions of Smoluchowski's coagulation equation with product kernel of homogeneity 2λ ∈ (0, 1). We establish rigorously that such solutions exhibit a singular behavior of the form x ?(1+2λ) as x → 0. This property had been conjectured, but only weaker results had been available up to now. |
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| Keywords: | Product kernel Self-similar solutions Smoluchowski's coagulation equations |
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