Global existence, boundedness and stabilization in a high-dimensional chemotaxis system with consumption

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

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  • J. Lankeit
  • Yulan Wang

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OriginalspracheEnglisch
Seiten (von - bis)6099-6121
Seitenumfang23
FachzeitschriftDiscrete and Continuous Dynamical Systems- Series A
Jahrgang37
Ausgabenummer12
PublikationsstatusVeröffentlicht - 2017

Abstract

This paper deals with the homogeneous Neumann boundary-value problem for the chemotaxis-consumption system (Equation presented)in N-dimensional bounded smooth domains for suitably regular positive initial data. We shall establish the existence of a global bounded classical solution for suitably large μ and prove that for any μ > 0 there exists a weak solution. Moreover, in the case of κ > 0 convergence to the constant equilibrium (κ/μ, 0) is shown.

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Global existence, boundedness and stabilization in a high-dimensional chemotaxis system with consumption. / Lankeit, J.; Wang, Yulan.
in: Discrete and Continuous Dynamical Systems- Series A, Jahrgang 37, Nr. 12, 2017, S. 6099-6121.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

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author = "J. Lankeit and Yulan Wang",
note = "Funding Information: gemeinschaft within the project Analysis of chemotactic cross-diffusion in complex frameworks. Y. Wang was supported by the NNSF of China (no. 11501457). Funding Information: J. Lankeit acknowledges support of the Deutsche Forschungsgemeinschaft within the project Analysis of chemotactic cross-diffusion in complex frameworks. Y. Wang was supported by the NNSF of China (no. 11501457). ∗ Corresponding author: Johannes Lankeit.",
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T1 - Global existence, boundedness and stabilization in a high-dimensional chemotaxis system with consumption

AU - Lankeit, J.

AU - Wang, Yulan

N1 - Funding Information: gemeinschaft within the project Analysis of chemotactic cross-diffusion in complex frameworks. Y. Wang was supported by the NNSF of China (no. 11501457). Funding Information: J. Lankeit acknowledges support of the Deutsche Forschungsgemeinschaft within the project Analysis of chemotactic cross-diffusion in complex frameworks. Y. Wang was supported by the NNSF of China (no. 11501457). ∗ Corresponding author: Johannes Lankeit.

PY - 2017

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N2 - This paper deals with the homogeneous Neumann boundary-value problem for the chemotaxis-consumption system (Equation presented)in N-dimensional bounded smooth domains for suitably regular positive initial data. We shall establish the existence of a global bounded classical solution for suitably large μ and prove that for any μ > 0 there exists a weak solution. Moreover, in the case of κ > 0 convergence to the constant equilibrium (κ/μ, 0) is shown.

AB - This paper deals with the homogeneous Neumann boundary-value problem for the chemotaxis-consumption system (Equation presented)in N-dimensional bounded smooth domains for suitably regular positive initial data. We shall establish the existence of a global bounded classical solution for suitably large μ and prove that for any μ > 0 there exists a weak solution. Moreover, in the case of κ > 0 convergence to the constant equilibrium (κ/μ, 0) is shown.

KW - Asymptotic stability

KW - Boundedness

KW - Chemotaxis

KW - Global existence

KW - Logistic source

KW - Weak solution

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