Abstract: |
The classical model for chemotaxis is the planar Keller-Segel system ut=Δu−∇⋅(u∇v),v(⋅,t)=12πlog1|⋅|∗u(⋅,t). in \R2×(0,∞). A blow-up of finite mass solutions is expected to occur by aggregation, a concentration of bubbling type, common to many geometric flows. We build with precise profiles solutions in the critical-mass case 8π, where blow-up takes place in infinite time. We establish the stability of the phenomenon detected under arbitrary mass-preserving small perturbations and present new constructions in the finite time blow-up scenario. The results presented are in collaboration with Federico Buseghin, Juan Davila, Jean Dolbeault, Monica Musso, and Juncheng Wei. |
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