Regularization and separation for evolving surface Cahn-Hilliard equations. (English) Zbl 1531.35328
This work considers the mathematical sides of the problem related to the biophysical phenomena of recent interest related to molecular transport and pattern formation on the cell membrane surface, which can be highly nonuniform itself. Thus, the authors address the Cahn-Hilliard equation when a constant mobility in a logarithmic potential is combined with an evolving surface. For the Cahn-Hilliard system in a weak variational formulation, regularization properties of weak solutions in finite time are proved. As a consequence potentially useful for the practical numerical treatment of the system, a suitable Galerkin approximation is proposed.
Reviewer: Eugene Postnikov (Kursk)
MSC:
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 92C37 | Cell biology |
| 35R01 | PDEs on manifolds |
| 58J90 | Applications of PDEs on manifolds |
| 35D30 | Weak solutions to PDEs |
| 35B65 | Smoothness and regularity of solutions to PDEs |
Keywords:
evolving surface; Cahn-Hilliard equation; logarithmic potential; instantaneous regularization; separation propertyReferences:
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