Scholarlink

<p>We focus on the derivation and analysis of a model for multi-component phase separation occurring on biological membranes, inspired by observations of lipid raft formation. The model integrates local membrane composition with local membrane curvature, describing the membrane’s geometry through a perturbation method represented as a graph over an undeformed Helfrich minimising surface, such as a sphere. The resulting energy consists of a small deformation functional coupled to a Cahn–Hilliard functional. By applying Onsager’s variational principle, we obtain a multi-component Cahn–Hilliard equation for the vector <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\varvec{\varphi }\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="bold-italic">φ</mi> </mrow> </math></EquationSource> </InlineEquation> of protein concentrations coupled to an evolution equation for the small deformation <i>u</i> along the normal direction to the reference membrane. Then, in the case of a constant mobility matrix, we consider the Cauchy problem and we prove that it is (globally) well posed in a weak setting. We also demonstrate that any weak solution regularises in finite time and satisfies the so-called “strict separation property”. This property allows us to show that any weak solution converges to a single stationary state by a suitable version of the Łojasiewicz–Simon inequality.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Multi-component phase separation and small deformations of a spherical biomembrane

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年2月17日

查看全文
  • Diogo Caetano,
  • Charles M. Elliott,
  • Maurizio Grasselli,
  • Andrea Poiatti

摘要

We focus on the derivation and analysis of a model for multi-component phase separation occurring on biological membranes, inspired by observations of lipid raft formation. The model integrates local membrane composition with local membrane curvature, describing the membrane’s geometry through a perturbation method represented as a graph over an undeformed Helfrich minimising surface, such as a sphere. The resulting energy consists of a small deformation functional coupled to a Cahn–Hilliard functional. By applying Onsager’s variational principle, we obtain a multi-component Cahn–Hilliard equation for the vector \(\varvec{\varphi }\) φ of protein concentrations coupled to an evolution equation for the small deformation u along the normal direction to the reference membrane. Then, in the case of a constant mobility matrix, we consider the Cauchy problem and we prove that it is (globally) well posed in a weak setting. We also demonstrate that any weak solution regularises in finite time and satisfies the so-called “strict separation property”. This property allows us to show that any weak solution converges to a single stationary state by a suitable version of the Łojasiewicz–Simon inequality.