debateGlobal existence and uniqueness of solutions to a
nasty nastychemotaxis systemadv
期刊名称： Applicable Analysis
作者： Aïssa, Naïma,Balehouane, Abdelkhalek
市场营销研究生>cereal怎么读
fallout shelter年份： 2019年
关键词： Roger Temam;Nonlinear diffusion;chemotaxis;Keller–Segel;quasilinear parabolic system;global existence;35K55;35K59;35Q92f man
摘要：This paper is dealing with the existence and uniqueness of a global in-time bounded solution to a quasilinear chemotaxis system ttled in a bounded domain under no-flux boundary conditions. The main difficulty occurs in the prence of the nonlinear logarithmic diffusion which can blow up around zero, and the energy estimates which do not provide a uniform estimate for large values of cell density u. Moreover, the chemo-nsitivity function depends on both cell and chemo-attractant densities which
prents a further difficulty while proving the global existence of a solution. This is overcome by tracking the time evolution of a suitable functional. The existence of local in-time weak solutions is ensured using Schauder's fixed point theorem, while the uniqueness is obtained by adapting the method introduced in Diaz et al. [应试教育英文
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