A PROBABILISTIC CONSIDERATION ON ONE DIMENSIONAL KELLER SEGEL SYSTEM

TitleA PROBABILISTIC CONSIDERATION ON ONE DIMENSIONAL KELLER SEGEL SYSTEM
Publication TypeJournal Article
Year of Publication2016
AuthorsYAHAGI YUMI
JournalNeural, Parallel, and Scientific Computations
Volume24
Start Page15
Pagination14
Date Published2016
ISSN1061-5369
Keywords35K15, 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.

URLhttps://acadsol.eu/npsc/articles/24/NPSC-15-28.pdf
Refereed DesignationRefereed