Uniqueness and symmetry of equilibria in a chemotaxis model
We consider in a disc a class of parameter-dependent,
nonlocal elliptic boundary value problems that describe the steady
states of some chemotaxis systems. If the appearing parameter is less
than an explicit critical value, we establish several uniqueness
results for solutions that are invariant under a group of
rotations. Furthermore, we discuss the associated consequences for the
time asymptotic behavior of the solutions to the corresponding time
dependent chemotaxis systems. Our results also provide optimal
constants in some Moser-Trudinger type inequalities.