Differential and Integral Equations

Global existence and decay estimates of solutions to a parabolic-elliptic system of drift-diffusion type in $\mathbb R^2$

Toshitaka Nagai

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Abstract

We consider a parabolic-elliptic system of drift-diffusion type in the entire two-dimensional Euclidean space, modeling chemotaxis and self-attracting particles. Under the assumption that the total mass of nonnegative initial data is less than $8\pi$, we give global existence and decay estimates of nonnegative solutions to the Cauchy problem for this system.

Article information

Source
Differential Integral Equations, Volume 24, Number 1/2 (2011), 29-68.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356019044

Mathematical Reviews number (MathSciNet)
MR2759351

Zentralblatt MATH identifier
1240.35066

Subjects
Primary: 35B45: A priori estimates 35K15: Initial value problems for second-order parabolic equations 35K55: Nonlinear parabolic equations

Citation

Nagai, Toshitaka. Global existence and decay estimates of solutions to a parabolic-elliptic system of drift-diffusion type in $\mathbb R^2$. Differential Integral Equations 24 (2011), no. 1/2, 29--68. https://projecteuclid.org/euclid.die/1356019044


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