Does the fully parabolic quasilinear 1D Keller-Segel system enjoy long-time asymptotics analogous to its parabolic-elliptic simplification?

Jan Burczak, Tomasz Cieślak, Cristian Morales-Rodrigo

We show that the one-dimensional fully parabolic Keller-Segel system with nonlinear diffusion possesses global-in-time solutions, provided the nonlinear diffusion is equal to (1+u)…