STABILITY OF STEADY-STATE SOLUTIONS OF A CLASS OF KELLER-SEGEL MODELS
WITH MIXED BOUNDARY CONDITIONS
Abstract
In this paper, we investigate the the existence and stability of
non-trivial steady state solutions of a class of chemotaxis models with
zero-flux boundary conditions and Dirichlet boundary conditions on
one-dimensional bounded interval. By using upper-lower solution and the
monotone iteration scheme method, we get the existence of the
steady-state solution of the chemotaxis model. Moreover, by adopting the
“inverse derivative” technique and the weighted energy method to
obtain the stability of the steady-state solution of this chemotaxis
model.