Article Dans Une Revue Applied Mathematics and Optimization Année : 2020

Cahn–Hilliard Models for Glial Cells

Résumé

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.

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Dates et versions

hal-04479855 , version 1 (27-02-2024)

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Lu Li, Alain Miranville, Rémy Guillevin. Cahn–Hilliard Models for Glial Cells. Applied Mathematics and Optimization, 2020, 84 (2), pp.1821-1842. ⟨10.1007/s00245-020-09696-x⟩. ⟨hal-04479855⟩
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