In this paper we consider radially symmetric solutions of the cross-diffusion system with flux limitation, under no flux boundary conditions and positive initial data. If N ≥ 3, under conditions on the data, we prove that the solution blows up in L∞-norm at finite time Tmax. Moreover for all p > N we prove that the solution blows up also in Lp-norm and a lower bound of blow-up time is derived.
Blow-up in a degenerate attraction-repulsion chemotaxis system with flux limitation
Monica Marras
;Stella Vernier-Piro;
2026-01-01
Abstract
In this paper we consider radially symmetric solutions of the cross-diffusion system with flux limitation, under no flux boundary conditions and positive initial data. If N ≥ 3, under conditions on the data, we prove that the solution blows up in L∞-norm at finite time Tmax. Moreover for all p > N we prove that the solution blows up also in Lp-norm and a lower bound of blow-up time is derived.
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