Asymptotic solutions to the Smoluchowski's coagulation equation with singular gamma distributions as initial size spectra
(2007) In Journal of Colloid and Interface Science 309(2). p.440444 Abstract
 Smoluchowski's coagulation equation is studied for the kernel K (u, v) = E(u(alpha)v(beta) + u(beta) v(alpha)) with real, nonnegative alpha, beta and E, using gamma distributions with a singularity at zero volume as initial size spectra. As the distribution parameter of the gamma distribution, p, approaches its lower limit (p > 0) the distribution becomes similar to pv(p1) 1 for small v. Asymptotic solutions to the coagulation equation are derived for the two cases p > 0 and v > 0. The constant kernel (alpha = beta = 0) is shown to be unique among the studied kernels in the sense that the p > 0 asymptote and the v 0 asymptote differ.
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/662600
 author
 Lindblad, Ulf ^{LU}
 organization
 publishing date
 2007
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 distribution, gamma, the Smoluchowski coagulation equation, exact solutions
 in
 Journal of Colloid and Interface Science
 volume
 309
 issue
 2
 pages
 440  444
 publisher
 Elsevier
 external identifiers

 wos:000245967700031
 scopus:34047250502
 ISSN
 10957103
 DOI
 10.1016/j.jcis.2006.09.072
 language
 English
 LU publication?
 yes
 id
 ddef57f0b8694bc68af5712d10f5f125 (old id 662600)
 date added to LUP
 20071213 11:41:42
 date last changed
 20180107 05:16:57
@article{ddef57f0b8694bc68af5712d10f5f125, abstract = {Smoluchowski's coagulation equation is studied for the kernel K (u, v) = E(u(alpha)v(beta) + u(beta) v(alpha)) with real, nonnegative alpha, beta and E, using gamma distributions with a singularity at zero volume as initial size spectra. As the distribution parameter of the gamma distribution, p, approaches its lower limit (p > 0) the distribution becomes similar to pv(p1) 1 for small v. Asymptotic solutions to the coagulation equation are derived for the two cases p > 0 and v > 0. The constant kernel (alpha = beta = 0) is shown to be unique among the studied kernels in the sense that the p > 0 asymptote and the v 0 asymptote differ.}, author = {Lindblad, Ulf}, issn = {10957103}, keyword = {distribution,gamma,the Smoluchowski coagulation equation,exact solutions}, language = {eng}, number = {2}, pages = {440444}, publisher = {Elsevier}, series = {Journal of Colloid and Interface Science}, title = {Asymptotic solutions to the Smoluchowski's coagulation equation with singular gamma distributions as initial size spectra}, url = {http://dx.doi.org/10.1016/j.jcis.2006.09.072}, volume = {309}, year = {2007}, }