Global Weak Solutions Of A Multi-scale Chemotaxis Model

In this thesis, we consider the multiscale hapotaxis-chemotaxis model: real number. We prove the global existence, along with some basic boundedness properties, of solutions to the approximate problem of the model, and then prove the global existence, along with some basic boundedness properties, of weak solutions to this model. Our main results of this paper are as follows: Let n≤3, and Ω￠Rn Rn be a bounded domain with smooth boundary and suppose that c0,υ0,l0,y10,y20,κ0,(?),(?),f, H satisfy certain conditions. Then the above problem possesses at least one global weak solution. Moreover, this solution has the following global boundedness properties:There exists C> 0 such that...