# A PROBABILISTIC CONSIDERATION ON ONE DIMENSIONAL KELLER SEGEL SYSTEM

 Title A PROBABILISTIC CONSIDERATION ON ONE DIMENSIONAL KELLER SEGEL SYSTEM Publication Type Journal Article Year of Publication 2016 Authors YAHAGI YUMI Journal Neural, Parallel, and Scientific Computations Volume 24 Start Page 15 Pagination 14 Date Published 2016 ISSN 1061-5369 Keywords 35K15, 60H10, 60H30 Abstract 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 ${ (u, v) }$ with  ${ u = u(x, t), \ v = v(x, t),}$ the solution of (KS), by means of expectation of functionals of the SDE, we derive a set of bounds for ${ (u, v)}$  which gives a good estimate of ${ (u, v) }$ around time zero. URL https://acadsol.eu/npsc/articles/24/NPSC-15-28.pdf Refereed Designation Refereed