A note on boundedness of solutions to a higher-dimensional quasi-linear chemotaxis system with logistic source

作者：Zheng, Jiashan^*

来源：ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik, 2017, 97(4): 414-421.

DOI：10.1002/zamm.201600166

• Boundedness
• chemotaxis
• global existence
• logistic source

We deal with the boundedness of solutions of a class of quasilinear chemotaxis systems generalizing the prototype
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where R-N(N = 3) is a bounded domain with smooth boundary, phi(u) = (u + 1)(alpha), psi(u) = u(u + 1)(beta 1). It is showed that if 0 < alpha + beta < 4/N+2, then for any sufficiently smooth initial data there exists a classical solution which is global in time and bounded. The novelty of the paper is that we use the boundedness of parallel to del v(., t)parallel to(L2(Omega)) to estimate the boundedness of parallel to del v(., t)parallel to(L2M(Omega)) (m > 1) which is different from [10] and [17]. The results of this paper partly improve the results of [10] and [17].

• 出版日期2017-4
• 单位鲁东大学