In this paper we study this chemotaxis-system defined in a convex smooth and bounded domain Ω of Rn, with n ≥ 1, and endowed with homogeneous Neumann boundary conditions, being χ > 0 and g a sort of logistic function obeying growth technical restrictions. Specifically, once an appropriate definition of very weak solution is given, our main result deals with the global existence of such solutions for any nonnegative initial data (u0,v0)∈ C0(Ω) × C2(Ω), and under zero-flux boundary condition on v0.
Very weak global solutions to a parabolic-parabolic chemotaxis-system with logistic source
VIGLIALORO, GIUSEPPE
2016-01-01
Abstract
In this paper we study this chemotaxis-system defined in a convex smooth and bounded domain Ω of Rn, with n ≥ 1, and endowed with homogeneous Neumann boundary conditions, being χ > 0 and g a sort of logistic function obeying growth technical restrictions. Specifically, once an appropriate definition of very weak solution is given, our main result deals with the global existence of such solutions for any nonnegative initial data (u0,v0)∈ C0(Ω) × C2(Ω), and under zero-flux boundary condition on v0.
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