MR Etsushi NAKAGUCHI and Koichi OSAKI Etsushi NAKAGUCHI and Koichi OSAKI $L_p$-Estimates of Solutions to $n$-Dimensional Parabolic-Parabolic System for Chemotaxis with Subquadratic Degradation Funkcialaj Ekvacioj. Serio Internacia 59 2016 51--66 http://fe.math.kobe-u.ac.jp/FE/FullPapers/59-1/59_51.pdf http://www.ams.org/mathscinet-getitem?mr=MR We study the global existence of solutions to an $n$-dimensional parabolic-parabolic system for chemotaxis with a subquadratic degradation. We introduce sublinear production of a chemoattractant. We then show the global existence of solutions in $L_p$ space $(p>n)$ under certain relations between the degradation and production orders. Chemotaxis, Logistic source, $L_p$-estimates, Global existence. Primary 35K51; Secondary 35A01, 35B45, 35K57, 35Q92, 92C17. 59-51 2016 $L_p$-Estimates of Solutions to $n$-Dimensional Parabolic-Parabolic System for Chemotaxis with Subquadratic Degradation Etsushi NAKAGUCHI and Koichi OSAKI Etsushi NAKAGUCHI and Koichi OSAKI
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