Curvature effects in pattern formation: well-posedness and optimal control of a sixth-order Cahn-Hilliard equation
DOI10.1137/24M1630372zbMATH Open1543.35092MaRDI QIDQ6571039
Gianni Gilardi, Jürgen Sprekels, Andrea Signori, Pierluigi Colli
Publication date: 11 July 2024
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
optimal controlwell-posednesscurvature effectsWillmore regularizationfirst-order necessary optimality conditionsfunctionalized Cahn-Hilliard equationsixth-order Cahn-Hilliard equation
Optimality conditions for problems involving partial differential equations (49K20) Nonlinear parabolic equations (35K55) Fréchet and Gateaux differentiability in optimization (49J50) Existence theories for optimal control problems involving partial differential equations (49J20) Initial-boundary value problems for second-order parabolic systems (35K51)
Cites Work
- Robust exponential attractors for the modified phase-field crystal equation
- On the phase-field-crystal model with logarithmic nonlinear terms
- A phase-field approximation of the Willmore flow with volume constraint
- A sixth order Cahn-Hilliard type equation arising in oil-water-surfactant mixtures
- A Cahn-Hilliard equation with singular diffusion
- Global smooth solutions of the three-dimensional modified phase field crystal equation
- The Willmore functional and instabilities in the Cahn-Hilliard equation
- On the Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions
- Compact sets in the space \(L^ p(0,T;B)\)
- A phase field approach in the numerical study of the elastic bending energy for vesicle membranes
- On a class of sixth order viscous Cahn-Hilliard type equations
- Existence of pearled patterns in the planar functionalized Cahn-Hilliard equation
- Existence, bifurcation, and geometric evolution of quasi-bilayers in the multicomponent functionalized Cahn-Hilliard equation
- Well-posedness and long-time behavior for the modified phase-field crystal equation
- A phase field formulation of the Willmore problem
- On a Higher Order Convective Cahn--Hilliard-Type Equation
- Sixth-order Cahn–Hilliard equations with singular nonlinear terms
- PEM Fuel Cells: A Mathematical Overview
- A new phase-field model for strongly anisotropic systems
- Robust exponential attractors for Cahn‐Hilliard type equations with singular potentials
- Global Weak Solutions to a Sixth Order Cahn--Hilliard Type Equation
- A Phase-Field Approximation of the Willmore Flow with Volume and Area Constraints
- On a Class of Sixth-Order Cahn--Hilliard-Type Equations with Logarithmic Potential
- Meander and Pearling of Single-Curvature Bilayer Interfaces in the Functionalized Cahn--Hilliard Equation
- Free Energy of a Nonuniform System. I. Interfacial Free Energy
- Competitive Geometric Evolution of Amphiphilic Interfaces
- Cahn–Hilliard–Brinkman model for tumor growth with possibly singular potentials
Related Items (1)
This page was built for publication: Curvature effects in pattern formation: well-posedness and optimal control of a sixth-order Cahn-Hilliard equation
Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6571039)
