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A new result for boundedness in the quasilinear parabolic-parabolic Keller-Segel model (with logistic source)
文献类型：期刊
通讯作者：Zheng, JS (reprint author), Ludong Univ, Sch Math & Stat Sci, Yantai 264025, Peoples R China.
期刊名称：COMPUTERS & MATHEMATICS WITH APPLICATIONS影响因子和分区
年：2020
卷：79
期：4
页码：1208-1221
ISSN：0898-1221
关键词：Boundedness; Keller-Segel; Parabolic-parabolic; Nonlinear diffusion
摘要：The current paper considers the boundedness of solutions to the following quasilinear Keller-Segel model (with logistic source) {u(t) = del . (D(u)del u) - chi del . (u del v) + mu(u - u(2)), x is an element of Omega, t > 0, v(t) - Delta v = u - v, x is an element of Omega, t > 0, (KS) (D(u)del u - chi u . del v) . nu = partial derivative v/partial derivative nu = 0, x is an element of partial derivative Omega, t > 0, u(x, 0) = u(0)(x), v(x, 0) = v(0)(x), x is an element of Omega, where Om ...More
The current paper considers the boundedness of solutions to the following quasilinear Keller-Segel model (with logistic source) {u(t) = del . (D(u)del u) - chi del . (u del v) + mu(u - u(2)), x is an element of Omega, t > 0, v(t) - Delta v = u - v, x is an element of Omega, t > 0, (KS) (D(u)del u - chi u . del v) . nu = partial derivative v/partial derivative nu = 0, x is an element of partial derivative Omega, t > 0, u(x, 0) = u(0)(x), v(x, 0) = v(0)(x), x is an element of Omega, where Omega subset of R-N(N >= 1) is a bounded domain with smooth boundary partial derivative Omega, chi > 0 and mu >= 0. One novelty of this paper is that we find a new a-priori estimate integral(Omega) u (chi max{1,lambda 0}/(chi max{1, lambda 0} - mu)+ - epsilon) (x, t)dx so that, we develop new L-p-estimate techniques and thereby obtain the boundedness results, where C-GN and lambda(0) := lambda(0)(gamma) are the constants which are corresponding to the Gagliardo-Nirenberg inequality (see Lemma 2.2) and the maximal Sobolev regularity (see Lemma 2.3). To our best knowledge, this seems to be the first rigorous mathematical result which indicates the relationship between m and mu/chi that yields the boundedness of the solutions, where m is the exponent of diffusion term D(u). The above -mentioned results have significantly improved and extended previous results of several authors. (C) 2019 Elsevier Ltd. All rights reserved. ...Hide

DOI：10.1016/j.camwa.2019.08.029
百度学术：A new result for boundedness in the quasilinear parabolic-parabolic Keller-Segel model (with logistic source)
语言：外文
基金：National Natural Science Foundation of ChinaNational Natural Science Foundation of China [11601215]; Shandong Provincial Science Foundation for Outstanding Youth [ZR2018JL005]; China Postdoctoral Science FoundationChina Postdoctoral Science Foundation [2019T120889, 2019M650927]
作者其他论文



An optimal result for global existence and boundedness in a three-dimensional Keller-Segel-Stokes system with nonlinear diffusion.Zheng, Jiashan,.JOURNAL OF DIFFERENTIAL EQUATIONS. 2019, 267(4), 2385-2415.
GLOBAL EXISTENCE AND BOUNDEDNESS OF SOLUTION OF A PARABOLIC-PARABOLIC-ODE CHEMOTAXIS-HAPTOTAXIS MODEL WITH (GENERALIZED) LOGISTIC SOURCE.Liu, Ling, Zheng, Jiashan,.DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B. 2019, 24(7), 3357-3377.
A new result for global solvability and boundedness in the N-dimensional quasilinear chemotaxis model with logistic for source and consumption of chemoattractant.Song, Xinchao, Zheng, Jiashan,.JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. 2019, 475(1), 895-917.
An optimal result for global existence in a three-dimensional Keller-Segel-Navier-Stokes system involving tensor-valued sensitivity with saturation.Ke, Yuanyuan, Zheng, Jiashan,.CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. 2019, 58(3).
A new result for 2D boundedness of solutions to a chemotaxis-haptotaxis model with/without sub-logistic source.Xiang, Tian, Zheng, Jiashan,.NONLINEARITY. 2019, 32(12), 4890-4911.