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- Publisher
- Springer Journals
- Copyright
- Copyright © Springer Science+Business Media, LLC, part of Springer Nature 2020
- ISSN
- 0095-4616
- eISSN
- 1432-0606
- DOI
- 10.1007/s00245-020-09696-x
- Publisher site
- See Article on Publisher Site
Abstract
Our aim in this paper is to study a Cahn–Hilliard model with a symport term. This equation is proposed to model some energy mechanisms (e.g., lactate) in glial cells. The main difficulty is to prove the existence of a biologically relevant solution. This is achieved by considering a modified equation and taking a logarithmic nonlinear term. A second difficulty is to prove additional regularity on the solutions which is essential to prove a strict separation from the pure states 0 and 1 in one and two space dimensions. We also consider a second model, based on the Cahn–Hilliard–Oono equation.
Journal
Applied Mathematics and Optimization – Springer Journals
Published: Oct 1, 2021
Keywords: Cahn–Hilliard equation; Cahn–Hilliard–Oono equation; Symport term; Logarithmic nonlinear term; Existence; Regularity; Strict separation; 35K55; 35B45; 35Q92