<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">WILSON LAMB</style></author><author><style face="normal" font="default" size="100%">ADAM  MCBRIDE</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A DISTRIBUTIONAL APPROACH TO FRAGMENTATION EQUATIONS</style></title></titles><keywords><keyword><style  face="normal" font="default" size="100%">45K05</style></keyword><keyword><style  face="normal" font="default" size="100%">46F05</style></keyword><keyword><style  face="normal" font="default" size="100%">47D06</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2011</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2011</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.acadsol.eu/en/articles/15/4/6.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">15</style></volume><pages><style face="normal" font="default" size="100%">10</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p class=&quot;rtejustify&quot;&gt;We consider a linear integro-differential equation that models multiple fragmentation with inherent mass-loss. A systematic procedure is presented for constructing a space of generalised functions Z′ in which initial-value problems involving singular initial conditions such as the Dirac delta distribution can be analysed. The procedure makes use of results on sun dual semigroups and quasi-equicontinuous semigroups on locally convex spaces. The existence and uniqueness of a distributional solution to an abstract version of the initial-value problem are established for any given initial data &lt;em&gt;u&lt;sub&gt;0&lt;/sub&gt;&lt;/em&gt; in Z′ .&lt;/p&gt;
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