MR2829547
Tetsuya YAMADA
Tetsuya YAMADA
Moment Estimates and Higher-Order Asymptotic Expansions of Solutions to a Parabolic System of Chemotaxis in the Whole Space
Funkcialaj Ekvacioj. Serio Internacia
54
2011
15--51
http://fe.math.kobe-u.ac.jp/FE/FullPapers/54-1/54_15.pdf
http://www.ams.org/mathscinet-getitem?mr=MR2829547
We study the asymptotic profiles of bounded solutions to the initial value problem for a parabolic system of chemotaxis. Very recently, it was shown in Yamada [18] that under suitable initial conditions, Theorem 2.1 of Yamada [17] also holds true for bounded solutions by deriving the moment estimate of $n$-th order for the solution. In this paper, we prove that if the $l$-th moment of initial data is finite for some $l \ge1$, then the bounded solution admits the moment estimate of $l$-th order. Moreover, as an application, we give the asymptotic profiles of bounded solutions by space-time higher-order asymptotic expansions under suitable moment conditions on the initial data.
Chemotaxis, Higher-order asymptotic expansion, Moment estimate.
35K45, 35B40, 35C20, 92C17.
54-15
2011
Moment Estimates and Higher-Order Asymptotic Expansions of Solutions to a Parabolic System of Chemotaxis in the Whole Space
Tetsuya YAMADA
Tetsuya YAMADA
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