This paper is composed of four chapters, which are independent and correlative to one another. In chaper 1, Sobolev space and upper and lower solutions are introduced. In section 1.1, we will introduce Sobolev space. In section 1.2, we will introduce upper and lower solutions of parabolic equation, In section 1.3, we will depict the background.In chaper 2, we set up a mathematical model of biodegradation. In section 2.1, we have the equations:In section 2.2, we give the preliminary knowledge.In chaper 3.1, we introduce the existence and uniqueness of time-dependent solution, the existence and uniqueness of steady-state solutions. The asymptotic behavior of time-dependent solution. |