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J. Korean Math. Soc. 2000; 37(6): 929-941

Printed November 1, 2000

Copyright © The Korean Mathematical Society.

Local and norm behavior of blowup solutions to a parabolic system of chemotaxis

Takasi Senba and Takashi Suzuki

Abstract

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We study a parabolic system of chemotaxis introduced by E. F. Keller and L. A. Segel. First, norm behaviors of the blow-up solution are proven. Then some kind of symmetry breaking and the concentration toward the boundary follow when the $L^1$ norm of the initial value is less than 8$\pi$. Meanwhile a method of rearrangement is proposed to prove an inequality of Trudinger-Moser's type.

Keywords: chemotaxis, parabolic system, blowup, rearrangement, Trudinger-Moser inequality

MSC numbers: 35K55, 35K57, 92C15, 92D15

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