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September/October 2011 Convergence to self-similar solutions for a parabolic-elliptic system of drift-diffusion type in $\mathbb R^2$
Toshitaka Nagai
Adv. Differential Equations 16(9/10): 839-866 (September/October 2011).

Abstract

We consider the Cauchy problem for a parabolic-elliptic system of drift-diffusion type in $\mathbb R^2$, modeling chemotaxis and self-attracting particles, with $L^1$-initial data. Under the assumption that the total mass of nonnegative initial data is less than $8\pi$, by using similarity arguments, it is shown that the nonnegative solution converges to a radially symmetric self-similar solution at rate $o(t^{-1+1/p})$ in the $L^p$-norm $(1\le p\le\infty)$ as time goes to infinity.

Citation

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Toshitaka Nagai. "Convergence to self-similar solutions for a parabolic-elliptic system of drift-diffusion type in $\mathbb R^2$." Adv. Differential Equations 16 (9/10) 839 - 866, September/October 2011.

Information

Published: September/October 2011
First available in Project Euclid: 17 December 2012

zbMATH: 1227.35118
MathSciNet: MR2850755

Subjects:
Primary: 35B40, 35K15, 35K55

Rights: Copyright © 2011 Khayyam Publishing, Inc.

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Vol.16 • No. 9/10 • September/October 2011
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