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Strong time periodic solutions to Keller-Segel systems: An approach by the quasilinear Arendt-Bu theorem
Journal of Differential Equations ( IF 2.4 ) Pub Date : 2020-07-01 , DOI: 10.1016/j.jde.2020.01.020
Matthias Hieber , Christian Stinner

Abstract It is shown that the classical as well as quasilinear Keller-Segel systems with non-degenerate diffusion possess for given T-periodic and sufficiently small forcing functions a unique, strong T-time periodic solution. The proof given relies on the existence of strong T-periodic solutions for the linearized system, its characterization in terms of maximal L p -regularity of the underlying operator and a quasilinear version of the Arendt-Bu Theorem. The latter is of independent interest and yields the existence of strong T-periodic solutions to general quasilinear evolution equations under suitable conditions on the operators and the forcing terms.

中文翻译:

Keller-Segel 系统的强时间周期解:拟线性 Arendt-Bu 定理的一种方法

摘要 结果表明,对于给定的 T 周期和足够小的强迫函数,具有非简并扩散的经典和拟线性 Keller-Segel 系统具有唯一的强 T 时间周期解。给出的证明依赖于线性化系统的强 T 周期解的存在,它的表征是根据底层算子的最大 L p 正则性和阿伦特-布定理的拟线性版本。后者是独立感兴趣的,并且在算子和强迫项的合适条件下产生一般拟线性演化方程的强 T 周期解的存在性。
更新日期:2020-07-01
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