For the singular Keller-Segel system on a half-line, a unique boundary spike-layer steady state exists and is nonlinearly asymptotically stable for all m≥0, provided χ is sufficiently large when m<1.
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Boundary spike-layer solutions of the singular Keller-Segel system: existence and stability
For the singular Keller-Segel system on a half-line, a unique boundary spike-layer steady state exists and is nonlinearly asymptotically stable for all m≥0, provided χ is sufficiently large when m<1.