Advances in Differential Equations
- Adv. Differential Equations
- Volume 16, Number 9/10 (2011), 839-866.
Convergence to self-similar solutions for a parabolic-elliptic system of drift-diffusion type in $\mathbb R^2$
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.
Article information
Source
Adv. Differential Equations Volume 16, Number 9/10 (2011), 839-866.
Dates
First available in Project Euclid: 17 December 2012
Permanent link to this document
https://projecteuclid.org/euclid.ade/1355703178
Mathematical Reviews number (MathSciNet)
MR2850755
Zentralblatt MATH identifier
1227.35118
Subjects
Primary: 35B40: Asymptotic behavior of solutions 35K15: Initial value problems for second-order parabolic equations 35K55: Nonlinear parabolic equations
Citation
Nagai, Toshitaka. Convergence to self-similar solutions for a parabolic-elliptic system of drift-diffusion type in $\mathbb R^2$. Adv. Differential Equations 16 (2011), no. 9/10, 839--866. https://projecteuclid.org/euclid.ade/1355703178