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Blow-up solutions for the steady state of the Keller-Segel system on Riemann surfaces
Mohameden Ahmedou, Thomas Bartsch, Zhengni Hu
We study the following Neumann boundary problem related to the stationary solutions of the Keller-Segel system, a basic model of chemotaxis phenomena: \[ \left\{\begin{array}{ll} -…
Partial Blow-up Phenomena in the Toda System on Riemann Surfaces
Zhengni Hu, Mohameden Ahmedou, Thomas Bartsch
This work studies the partial blow-up phenomena for the Toda system on compact Riemann surfaces with smooth boundary. We consider the following coupled Liouville system wit…
Blow-up solutions for mean field equations with Neumann boundary conditions on Riemann surfaces
Zhengni Hu, Thomas Bartsch, Mohameden Ahmedou
On a compact Riemann surface with a smooth boundary , we consider the following mean field equations with Neumann boundary conditions: $$ -Δ_g u = λ\left(\frac…
On Solutions for Singular Toda System on Riemann Surfaces with Boundary
Zhengni Hu
This paper studies solutions to a singular Toda system with linear source terms on a compact Riemann surface with smooth boundaries . We establish the existe…
The Morse property of limit functions appearing in mean field equations on surfaces with boundary
Zhengni Hu, Thomas Bartsch
In this paper we study the Morse property for functions related to limit functions of mean field equations on a smooth, compact surface with boundary . Given a Riema…