Geodesic
Boundedness in a quasilinear parabolic-parabolic chemotaxis system with nonlinear logistic source
Czechoslovak Mathematical Journal, Tome 65 (2015) no. 4, pp. 1117-1136.

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We study a quasilinear parabolic-parabolic chemotaxis system with nonlinear logistic source, under homogeneous Neumann boundary conditions in a smooth bounded domain. By establishing proper a priori estimates we prove that, with both the diffusion function and the chemotaxis sensitivity function being positive, the corresponding initial boundary value problem admits a unique global classical solution which is uniformly bounded. The result of this paper is a generalization of that of Cao (2014).
DOI : 10.1007/s10587-015-0231-0
Classification : 35K59, 92C17
Keywords: boundedness; chemotaxis; nonlinear logistic source 
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     title = {Boundedness in a quasilinear parabolic-parabolic chemotaxis system with nonlinear logistic source},
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Liu, Ji; Zheng, Jia-Shan. Boundedness in a quasilinear parabolic-parabolic chemotaxis system with nonlinear logistic source. Czechoslovak Mathematical Journal, Tome 65 (2015) no. 4, pp. 1117-1136. doi : 10.1007/s10587-015-0231-0. http://geodesic.mathdoc.fr/articles/10.1007/s10587-015-0231-0/

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