Abstract
This paper deals with an initial-boundary value problem for the chemotaxis system
under homogeneous Neumann boundary conditions in a convex smooth bounded domain \({\Omega\subset \mathbb{R}^n}\) with \({n\geq3}\), where the diffusion function D(u) satisfying
with some c D > 0 and m > 1. The main goal of this paper was to extend a previous result on global existence of solutions by Wang et al. (Z Angew Math Phys 65:1137–1152, 2014) under the condition that \({m > 2-\frac{2}{n}}\) can be relaxed to \({m > 2-\frac{6}{n+4}}\).
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Wang, L., Mu, C., Lin, K. et al. Global existence to a higher-dimensional quasilinear chemotaxis system with consumption of chemoattractant. Z. Angew. Math. Phys. 66, 1633–1648 (2015). https://doi.org/10.1007/s00033-014-0491-9
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DOI: https://doi.org/10.1007/s00033-014-0491-9