On the existence of solutions of the Helfrich flow and its center manifold near spheres.

zbMath1212.49059MaRDI QIDQ601540

Yoshihito Kohsaka, Takeyuki Nagasawa

Publication date: 28 October 2010

Published in: Differential and Integral Equations (Search for Journal in Brave)

zbMATH Keywords

Lagrange multipliersLaplace-Beltrami operatorGaussian curvatureHelfrich variational problemhuman red blood cell

Mathematics Subject Classification ID

Optimization of shapes other than minimal surfaces (49Q10) Surfaces in Euclidean and related spaces (53A05) Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems (37L10) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

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Gradient flow for the Helfrich functional ⋮ Local well-posedness for relaxational fluid vesicle dynamics ⋮ The evolution of a class of curve flows ⋮ A note on singularities in finite time for the \(L^{2}\) gradient flow of the Helfrich functional ⋮ A curve flow evolved by a fourth order parabolic equation

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