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Analysis of a PDE model of the swelling of mitochondria accounting for spatial movement
Author(s) -
Efendiev Messoud A.,
Ôtani Mitsuharu,
Eberl Hermann J.
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4742
Subject(s) - swelling , mathematics , work (physics) , diffusion , process (computing) , diffusion process , biological system , statistical physics , computer science , thermodynamics , physics , materials science , knowledge management , innovation diffusion , composite material , operating system , biology
We analyze existence and asymptotic behavior of a system of semilinear diffusion‐reaction equations that arises in the modeling of the mitochondrial swelling process. The model itself expands previous work in which the mitochondria were assumed to be stationary, whereas now their movement is modeled by linear diffusion. While in the previous model certain formal structural conditions were required for the rate functions describing the swelling process, we show that these are not required in the extended model. Numerical simulations are included to visualize the solutions of the new model and to compare them with the solutions of the previous model.