A PROBABILISTIC CONSIDERATION ON ONE DIMENSIONAL KELLER SEGEL SYSTEM

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.