Stability of Lamellar Configurations in a Nonlocal Sharp Interface Model

DOI10.1137/21M1394321zbMath1481.49004OpenAlexW4206099355MaRDI QIDQ5024688

Emilio Acerbi, Chao-Nien Chen, Yung-Sze Choi

Publication date: 27 January 2022

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/21m1394321

zbMATH Keywords

stabilitysharp interface modellamellanonlocal geometric variational problem

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Reaction-diffusion equations (35K57) Developmental biology, pattern formation (92C15) Optimization of shapes other than minimal surfaces (49Q10) Existence theories for optimal control problems involving partial differential equations (49J20)

Cites Work

• Unnamed Item
• Unnamed Item
• Minimality via second variation for a nonlocal isoperimetric problem
• Dissipative solitons in reaction diffusion systems. Mechanisms, dynamics, interaction
• Traveling pulse solutions to Fitzhugh-Nagumo equations
• Periodic phase separation: the periodic Cahn-Hilliard and isoperimetric problems
• A second order minimality condition for the Mumford-Shah functional
• Some mathematical aspects of the micro-phase separation in diblock copolymers
• Pulse dynamics in a three-component system: Existence analysis
• On energy minimizers of the diblock copolymer problem
• On the derivation of a density functional theory for microphase separation of diblock copolymers
• Bubbles and droplets in a singular limit of the FitzHugh-Nagumo system
• Localized patterns in a three-component Fitzhugh-Nagumo model revisited via an action functional
• Standing pulse solutions to FitzHugh-Nagumo equations
• The gradient theory of phase transitions and the minimal interface criterion
• Optimal periodic structures with general space group symmetries in the Ohta-Kawasaki problem
• Minimal lamellar structures in a periodic FitzHugh-Nagumo system
• The \(\Gamma\)-limit of traveling waves in the FitzHugh-Nagumo system
• Coarsening fronts
• Traveling waves for the Fitzhugh-Nagumo system on an infinite channel
• The Nishiura--Ohnishi Free Boundary Problem in the 1D Case
• Cascade of Minimizers for a Nonlocal Isoperimetric Problem in Thin Domains
• Uniform energy distribution for an isoperimetric problem with long-range interactions
• Small Volume-Fraction Limit of the Diblock Copolymer Problem: II. Diffuse-Interface Functional
• On the Spectra of Three-Dimensional Lamellar Solutions of the Diblock Copolymer Problem
• On the Multiplicity of Solutions of Two Nonlocal Variational Problems
• Rigorously Computing Symmetric Stationary States of the Ohta--Kawasaki Problem in Three Dimensions
• Higher Dimensional Bubble Profiles in a Sharp Interface Limit of the FitzHugh--Nagumo System
• Validation of the bifurcation diagram in the 2D Ohta–Kawasaki problem
• Small Volume Fraction Limit of the Diblock Copolymer Problem: I. Sharp-Interface Functional
• Planar Standing Wavefronts in the FitzHugh--Nagumo Equations
• On the first and second variations of a nonlocal isoperimetric problem
• Periodicity and Uniqueness of Global Minimizers of an Energy Functional Containing a Long-Range Interaction
• Droplet phases in non-local Ginzburg-Landau models with Coulomb repulsion in two dimensions