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The Swelling of Mitochondria: Degenerate Diffusion

In: Mathematical Modeling of Mitochondrial Swelling

Author

Listed:
  • Messoud Efendiev

    (Helmholtz Center Munich, Institute of Computational Biology)

Abstract

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.

Suggested Citation

  • Messoud Efendiev, 2018. "The Swelling of Mitochondria: Degenerate Diffusion," Springer Books, in: Mathematical Modeling of Mitochondrial Swelling, chapter 0, pages 187-206, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-99100-9_6
    DOI: 10.1007/978-3-319-99100-9_6
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