Gradient flow dynamics for cell membranes in the Canham-Helfrich model

Fuente: arXiv
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Main Authors: Rupp, Fabian, Scharrer, Christian, Schlierf, Manuel
Format: Preprint
Published: 2024
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author Rupp, Fabian
Scharrer, Christian
Schlierf, Manuel
author_facet Rupp, Fabian
Scharrer, Christian
Schlierf, Manuel
contents The energetically most efficient way how a deformed red blood cell regains equilibrium is mathematically described by the gradient flow of the Canham-Helfrich functional, including a spontaneous curvature and the conservation of surface area and enclosed volume. Using a recently discovered multiplicity inequality, we prove global existence and convergence of smooth solutions for spheres and axisymmetric tori, provided the initial energy lies below explicit thresholds.
format Preprint
id arxiv_https___arxiv_org_abs_2408_07493
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Gradient flow dynamics for cell membranes in the Canham-Helfrich model
Rupp, Fabian
Scharrer, Christian
Schlierf, Manuel
Analysis of PDEs
Differential Geometry
53E40 (primary), 35B40, 49Q10 (secondary)
The energetically most efficient way how a deformed red blood cell regains equilibrium is mathematically described by the gradient flow of the Canham-Helfrich functional, including a spontaneous curvature and the conservation of surface area and enclosed volume. Using a recently discovered multiplicity inequality, we prove global existence and convergence of smooth solutions for spheres and axisymmetric tori, provided the initial energy lies below explicit thresholds.
title Gradient flow dynamics for cell membranes in the Canham-Helfrich model
topic Analysis of PDEs
Differential Geometry
53E40 (primary), 35B40, 49Q10 (secondary)
url https://arxiv.org/abs/2408.07493