Asymptotic behavior of solutions to a quasilinear nonuniform parabolic system modelling chemotaxis

作者：Zhang Yanyan^*; Zheng Songmu

来源：Journal of Differential Equations, 2010, 248(7): 1684-1710.

DOI：10.1016/j.jde.2009.09.021

• Chemotaxis
• Volume-filling effect
• Quasilinear nonuniform parabolic system
• Uniform boundedness
• Convergence to equilibrium
• Non-smooth Simon-Lojasiewicz approach

in this paper. we Study a quasilinear nonuniform parabolic system modelling chemotaxis and taking the volume-filling effect into account. The results on the existence of a unique global classical solution was obtained in Cieslak (2007) [4]. However, the convergence to equilibrium was not considered in that paper. In this paper. we first obtain the crucial uniform boundedness of the Solution. Then with the help of a suitable non-smooth Simon-Lojasiewicz approach we obtain the results on convergence to equilibrium and the decay rate.

• 出版日期2010-4-1
• 单位复旦大学