Under suitable assumptions on parameters, the chemotaxis system admits a unique positive entire solution that is globally asymptotically stable.
Nagai, Blow-up of radially symmetric solutions of a c hemotaxis system, Adv
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Uniqueness and nonlinear stability of positive entire solutions in parabolic-parabolic chemotaxis models with logistic source on bounded heterogeneous environments
Under suitable assumptions on parameters, the chemotaxis system admits a unique positive entire solution that is globally asymptotically stable.