In this paper we consider nonnegative solutions of the following parabolic-elliptic cross-diffusion system [Formula presented] in Ω×(0,∞), with Ω a ball in RN, N≥3 under homogeneous Neumann boundary conditions and f(ξ)=(1+ξ)−α, [Formula presented], which describes gradient-dependent limitation of cross diffusion fluxes. Under conditions on f and initial data, we prove that a solution which blows up in finite time in L∞-norm, blows up also in Lp-norm for some p>1. Moreover, a lower bound of blow-up time is derived.

Blow-up phenomena for a chemotaxis system with flux limitation

Marras M.
;
Vernier-Piro S.;
2022

Abstract

In this paper we consider nonnegative solutions of the following parabolic-elliptic cross-diffusion system [Formula presented] in Ω×(0,∞), with Ω a ball in RN, N≥3 under homogeneous Neumann boundary conditions and f(ξ)=(1+ξ)−α, [Formula presented], which describes gradient-dependent limitation of cross diffusion fluxes. Under conditions on f and initial data, we prove that a solution which blows up in finite time in L∞-norm, blows up also in Lp-norm for some p>1. Moreover, a lower bound of blow-up time is derived.
Chemotaxis; Finite-time blow-up
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/344237
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