<?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%">YUMI YAHAGI</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A PROBABILISTIC CONSIDERATION ON ONE DIMENSIONAL KELLER SEGEL SYSTEM</style></title><secondary-title><style face="normal" font="default" size="100%">Neural, Parallel, and Scientific Computations</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">35K15</style></keyword><keyword><style  face="normal" font="default" size="100%">60H10</style></keyword><keyword><style  face="normal" font="default" size="100%">60H30</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2016</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2016</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/npsc/articles/24/NPSC-15-28.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">24</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper, we perform a consideration on partial differential equations known as the Keller Segel system (KS) through both probabilistic and numerical methods. Stochastic differential equation (SDE), having a correspondence with (KS) is the main tool of our probabilistic consideration. In our main theorem, by using probabilistic expressions of ${ (u, v) }$&amp;nbsp;with&amp;nbsp;&amp;nbsp;${ u = u(x, t), \&amp;nbsp; v = v(x, t),}$ the solution of (KS), by means of expectation of functionals of the SDE, we derive a set of bounds for ${ (u, v)}$&amp;nbsp; which gives a good estimate of ${ (u, v) }$ around time zero.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">15</style></section></record></records></xml>