Rigorously Computing Symmetric Stationary States of the Ohta--Kawasaki Problem in Three Dimensions
From MaRDI portal
Publication:4614397
DOI10.1137/17M1155624zbMath1409.35080MaRDI QIDQ4614397
No author found.
Publication date: 31 January 2019
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Nonlinear elliptic equations (35J60) PDEs in connection with mechanics of deformable solids (35Q74)
Related Items (14)
Microscopic patterns in the 2D phase-field-crystal model ⋮ Transition pathways in Cylinder-Gyroid interface ⋮ Equilibrium validation for triblock copolymers via inverse norm bounds for fourth-order elliptic operators ⋮ Efficient numerical scheme for a penalized Allen-Cahn type Ohta-Kawasaki phase-field model for diblock copolymers ⋮ Efficient approaches for verifying the existence and bound of inverse of linear operators in Hilbert spaces ⋮ Validated numerical approximation of stable manifolds for parabolic partial differential equations ⋮ Spontaneous periodic orbits in the Navier-Stokes flow ⋮ Equilibrium validation in models for pattern formation based on Sobolev embeddings ⋮ The Cahn-Hilliard equation with a nonlinear source term ⋮ Thermodynamically consistent algorithms for models of diblock copolymer solutions interacting with electric and magnetic fields ⋮ Global dynamics in nonconservative nonlinear Schrödinger equations ⋮ Rigorous validation of stochastic transition paths ⋮ Stability of Lamellar Configurations in a Nonlocal Sharp Interface Model ⋮ Optimal periodic structures with general space group symmetries in the Ohta-Kawasaki problem
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Computer-assisted equilibrium validation for the diblock copolymer model
- Analytic estimates and rigorous continuation for equilibria of higher-dimensional PDEs
- Rigorous continuation of bifurcation points in the diblock copolymer equation
- Rigorous numerics for ill-posed PDEs: periodic orbits in the Boussinesq equation
- Sufficient conditions for global minimality of metastable states in a class of non-convex functionals: a simple approach via quadratic lower bounds
- The \(\Gamma\)-limit of the two-dimensional Ohta-Kawasaki energy. Droplet arrangement via the renormalized energy
- Rigorous numerics for analytic solutions of differential equations: the radii polynomial approach
- Rigorous Numerics in Dynamics
- Verification methods: Rigorous results using floating-point arithmetic
- Small Volume-Fraction Limit of the Diblock Copolymer Problem: II. Diffuse-Interface Functional
- Validated Continuation for Equilibria of PDEs
- Chaotic Braided Solutions via Rigorous Numerics: Chaos in the Swift–Hohenberg Equation
- On the Phase Diagram for Microphase Separation of Diblock Copolymers: An Approach via a Nonlocal Cahn–Hilliard Functional
- Introduction to rigorous numerics in dynamics: General functional analytic setup and an example that forces chaos
- Numerical Computations and Computer Assisted Proofs of Periodic Orbits of the Kuramoto--Sivashinsky Equation
- Validation of the bifurcation diagram in the 2D Ohta–Kawasaki problem
- 2D Phase Diagram for Minimizers of a Cahn–Hilliard Functional with Long-Range Interactions
- A Posteriori Verification of Invariant Objects of Evolution Equations: Periodic Orbits in the Kuramoto--Sivashinsky PDE
This page was built for publication: Rigorously Computing Symmetric Stationary States of the Ohta--Kawasaki Problem in Three Dimensions
