This chapter consists of two subsections, and we consider the effect of degenerate diffusion on mitochondria swelling behavior. In Sect. 6.1 we study the well posedness of solutions under homogeneous Dirichlet boundary conditions. Note that we cannot apply the methods developed in the previous chapters for nondegenerate diffusion and new methods have been developed in order to study both well posedness and asymptotic behavior of solutions. In this section we show that the calcium ion concentration will tend to zero and that, in general, complete swelling will not take place as time goes to infinity in the case of degenerate diffusion. Section 6.2 gives numerical simulations.