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Ultra-contractivity for keller-segel model with diffusion exponent m > 1-2/d

Publication ,  Journal Article
Bian, S; Liu, JG; Zou, C
Published in: Kinetic and Related Models
March 1, 2014

This paper establishes the hyper-contractivity in L∞(ℝd) (it's known as ultra-contractivity) for the multi-dimensional Keller-Segel systems with the diffusion exponent m > 1-2/d. The results show that for the super- critical and critical case 1-2/d < m ≤ 2-2/d, if ∥U0∥d(2-m)/2 < Cd, m where Cd, m is a universal constant, then for any t > 0 ∥u(.,t)∥L∞(ℝd) is bounded and decays as t goes to infinity. For the subcritical case m > 2-2/d, the solution u(.,t)∈ L∞(ℝd) with any initial data U0 ∈ L1+(ℝd) for any positive time.

Duke Scholars

Published In

Kinetic and Related Models

DOI

EISSN

1937-5077

ISSN

1937-5093

Publication Date

March 1, 2014

Volume

7

Issue

1

Start / End Page

9 / 28

Related Subject Headings

  • Applied Mathematics
 

Citation

APA
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ICMJE
MLA
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Bian, S., Liu, J. G., & Zou, C. (2014). Ultra-contractivity for keller-segel model with diffusion exponent m > 1-2/d. Kinetic and Related Models, 7(1), 9–28. https://doi.org/10.3934/krm.2014.7.9
Bian, S., J. G. Liu, and C. Zou. “Ultra-contractivity for keller-segel model with diffusion exponent m > 1-2/d.” Kinetic and Related Models 7, no. 1 (March 1, 2014): 9–28. https://doi.org/10.3934/krm.2014.7.9.
Bian S, Liu JG, Zou C. Ultra-contractivity for keller-segel model with diffusion exponent m > 1-2/d. Kinetic and Related Models. 2014 Mar 1;7(1):9–28.
Bian, S., et al. “Ultra-contractivity for keller-segel model with diffusion exponent m > 1-2/d.” Kinetic and Related Models, vol. 7, no. 1, Mar. 2014, pp. 9–28. Scopus, doi:10.3934/krm.2014.7.9.
Bian S, Liu JG, Zou C. Ultra-contractivity for keller-segel model with diffusion exponent m > 1-2/d. Kinetic and Related Models. 2014 Mar 1;7(1):9–28.

Published In

Kinetic and Related Models

DOI

EISSN

1937-5077

ISSN

1937-5093

Publication Date

March 1, 2014

Volume

7

Issue

1

Start / End Page

9 / 28

Related Subject Headings

  • Applied Mathematics