Self-similar solutions to coagulation equations with time-dependent tails: The case of homogeneity smaller than one
| Autor: | Juan J. L. Velázquez, Barbara Niethammer, Marco Bonacini |
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| Rok vydání: | 2018 |
| Předmět: |
Class (set theory)
Pure mathematics Applied Mathematics Homogeneity (statistics) 010102 general mathematics Self-similar solutions Smoluchowski’s equation time-dependent tails 01 natural sciences 010101 applied mathematics Mathematics - Analysis of PDEs FOS: Mathematics Coagulation (water treatment) 0101 mathematics Analysis Analysis of PDEs (math.AP) Mathematics |
| Zdroj: | Communications in Partial Differential Equations. 43:82-117 |
| ISSN: | 1532-4133 0360-5302 |
| DOI: | 10.1080/03605302.2018.1437447 |
| Popis: | We prove the existence of a one-parameter family of self-similar solutions with time-dependent tails for Smoluchowski's coagulation equation, for a class of rate kernels $K(x,y)$ which are homogeneous of degree $\gamma\in(-\infty,1)$ and satisfy $K(x,1)\sim x^{-a}$ as $x\to 0$, for $a=1-\gamma$. In particular, for small values of a parameter $\rho>0$ we establish the existence of a positive self-similar solution with finite mass and asymptotics $A(t)x^{-(2+\rho)}$ as $x\to\infty$, with $A(t)\sim\rho t^\frac{\rho}{1-\gamma}$. |
| Databáze: | OpenAIRE |
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