### Abstract

The following degenerate parabolic system modelling chemotaxis is considered:{A formula is presented} where m {greater than or slanted equal to} 1, q {greater than or slanted equal to} 2, τ = 0 or 1, and N {greater than or slanted equal to} 1. The aim of this paper is to prove the existence of a time global weak solution ( u, v) of (KS) with the L^{∞} ( 0, ∞ ; L^{∞} ( R^{N} ) ) bound. Such a global bound is obtained in the case of (i) m > q - frac(2, N) for large initial data and (ii) 1 {less-than or slanted equal to} m {less-than or slanted equal to} q - frac(2, N) for small initial data. In the case of (ii), the decay properties of the solution ( u, v ) are also discussed.

Original language | English |
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Pages (from-to) | 333-364 |

Number of pages | 32 |

Journal | Journal of Differential Equations |

Volume | 227 |

Issue number | 1 |

DOIs | |

Publication status | Published - Aug 1 2006 |

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### All Science Journal Classification (ASJC) codes

- Analysis

### Cite this

*Journal of Differential Equations*,

*227*(1), 333-364. https://doi.org/10.1016/j.jde.2006.03.003

**Global existence and decay properties for a degenerate Keller-Segel model with a power factor in drift term.** / Sugiyama, Yoshie; Kunii, Hiroko.

Research output: Contribution to journal › Letter

*Journal of Differential Equations*, vol. 227, no. 1, pp. 333-364. https://doi.org/10.1016/j.jde.2006.03.003

}

TY - JOUR

T1 - Global existence and decay properties for a degenerate Keller-Segel model with a power factor in drift term

AU - Sugiyama, Yoshie

AU - Kunii, Hiroko

PY - 2006/8/1

Y1 - 2006/8/1

N2 - The following degenerate parabolic system modelling chemotaxis is considered:{A formula is presented} where m {greater than or slanted equal to} 1, q {greater than or slanted equal to} 2, τ = 0 or 1, and N {greater than or slanted equal to} 1. The aim of this paper is to prove the existence of a time global weak solution ( u, v) of (KS) with the L∞ ( 0, ∞ ; L∞ ( RN ) ) bound. Such a global bound is obtained in the case of (i) m > q - frac(2, N) for large initial data and (ii) 1 {less-than or slanted equal to} m {less-than or slanted equal to} q - frac(2, N) for small initial data. In the case of (ii), the decay properties of the solution ( u, v ) are also discussed.

AB - The following degenerate parabolic system modelling chemotaxis is considered:{A formula is presented} where m {greater than or slanted equal to} 1, q {greater than or slanted equal to} 2, τ = 0 or 1, and N {greater than or slanted equal to} 1. The aim of this paper is to prove the existence of a time global weak solution ( u, v) of (KS) with the L∞ ( 0, ∞ ; L∞ ( RN ) ) bound. Such a global bound is obtained in the case of (i) m > q - frac(2, N) for large initial data and (ii) 1 {less-than or slanted equal to} m {less-than or slanted equal to} q - frac(2, N) for small initial data. In the case of (ii), the decay properties of the solution ( u, v ) are also discussed.

UR - http://www.scopus.com/inward/record.url?scp=33646542023&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33646542023&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2006.03.003

DO - 10.1016/j.jde.2006.03.003

M3 - Letter

VL - 227

SP - 333

EP - 364

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 1

ER -