Boundary spike‐layer solutions of the singular Keller–Segel system: existence and stability
Boundary spike‐layer solutions of the singular Keller–Segel system: existence and stability
We explore the existence and nonlinear stability of boundary spike-layer solutions of the Keller–Segel system with logarithmic singular sensitivity in the half space, where the physical zero-flux and Dirichlet boundary conditions are prescribed. We first prove that, under above boundary conditions, the Keller–Segel system admits a unique boundary spike-layer steady …