Boundedness in a fully parabolic chemotaxis-consumption system with nonlinear diffusion and sensitivity, and logistic source

Giuseppe Viglialoro

;Monica Marras

2018-01-01

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Abstract

In this paper we study the zero-flux chemotaxis-system (Formula presented.) Ω being a convex smooth and bounded domain of ℝn, n≥1, and where m,k∈ℝ, μ > 0 and α 0. We prove that for nonnegative and sufficiently regular initial data u(x, 0) and v(x, 0), the corresponding initial-boundary value problem admits a unique globally bounded classical solution provided μ is large enough.