Nonlinear stability of diffusive contact wave for a chemotaxis model

Zeng, Yanni

doi:10.1016/j.jde.2021.11.008

Cited by 11 publications

(2 citation statements)

References 29 publications

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“…where m > 0 is the chemical consumption rate, which was aimed at describing the initiation of tumor angiogenesis. The Keller-Segel model with logarithmic sensitively term has been studied in [12,31,24,33,30,27]. It has been shown that when 0 ≤ m < 1, the system (2) has traveling bands; when m = 1, the system (2) has traveling fronts; when m > 1, the system (2) has no traveling waves.…”

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confidence: 99%

“…Besides, they studied the asymptotic behavior of solutions by developing the framework of entropy and energy estimate. Some researches often chose Hopf-Cole transformation to transform the logarithmic sensitivity system into a system of conservation laws and studied the existence of traveling wave solutions for the transformed system [2,21,30,19,11,20]. Du et al [7] considered the traveling pulse solution of one-dimensional generalized Keller-Segel model with small cell diffusion…”

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confidence: 99%

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Asymptotic behaviors and existence of traveling wave solutions to the Keller-Segel model with logarithmic sensitivity

Liu

2023

DCDS-B

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<p style='text-indent:20px;'>In this paper, we are concerned with the existence of traveling wave solutions for the Keller-Segel model with logarithmic sensitivity. By the Hopf-Cole transformation and traveling wave transformation, the degenerate Keller-Segel system is transformed into a singularly perturbed system. By constructing an invariant region to prove the existence of the traveling wave solutions for the degenerate system, we obtain the traveling wave solutions for Keller-Segel system with small parameter by using geometric singular perturbation theory and Fredholm theory. Finally, we discuss the asymptotic behaviors of the traveling wave solutions.</p>

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confidence: 99%