The mathematical models considered in this book can help to understand the swelling of mitochondria. For the first time, it presents new mathematical models of mitochondrial swelling that take into account, in particular, spatial effects. The results presented here could make it possible to predict properties of the underlying biological mechanisms. Taking into account that mitochondria could move within a cell, lead to a PDE-PDE model. The book discusses the well-posedness and long-term dynamics of solutions, depending on boundary conditions reflecting the in vitro and in vivo cases. These analytical and numerical results have inspired colleagues from the Institute of Pharmacology and Toxicology of the Helmholtz Center Munich to design new experiments justifying the theoretical and numerical results that are obtained. The book is intended for graduates students and researchers with a solid mathematical background and an interest in cell biology.

Professor Messoud Efendiev has been a major player and scientific leader in the field of infinite dimensional dynamical systems with applications to the life sciences, especially in biology, medicine and ecology. He has an extensive international collaborative network, formed during his graduate training at the Lomonosov Moscow State University, his AvH Fellowship at the University of Stuttgart, his postdoctoral studies at the Freie Universität Berlin, and his further career, including at the DFG Collaborative Research Center and the Helmholtz Center Munich. He is the recipient of various international fellowships and awards from Japan and Europe and has been a much sought-after speaker at major international research colloquia and conferences. Professor Efendiev was the first Azerbaijani scientist to be awarded the prestigious Feodor Lynen Research Fellowship for experienced researchers by the Alexander von Humboldt Foundation. He has collaborated with many distinguished mathematicians in many countries. In 2018 he held the Deans Distinguished Visiting Professorship, a joint program of the Fields Institute with the Faculty of Arts and Science and the Department of Mathematics at the University of Toronto.