A Cahn-Hilliard system with forward-backward dynamic boundary condition and non-smooth potentials
DOI10.1007/s00028-022-00847-xzbMath1501.35250arXiv2208.00664OpenAlexW4308563072MaRDI QIDQ2095439
Pierluigi Colli, Luca Scarpa, Takeshi Fukao
Publication date: 16 November 2022
Published in: Journal of Evolution Equations (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2208.00664
asymptoticswell-posednesstransmission problemforward-backward equationbackward heat equation on the boundarynon-smooth potentials
Dynamics of phase boundaries in solids (74N20) Stefan problems, phase changes, etc. (80A22) Perturbations in context of PDEs (35B20) Weak solutions to PDEs (35D30) Higher-order parabolic equations (35K25) Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations (35K61)
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Cites Work
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- Passage to the limit over small parameters in the viscous Cahn-Hilliard equation
- Monotonicity methods for nonlinear diffusion equations and their approximations with error estimates
- A Cahn-Hilliard model in a domain with non-permeable walls
- Asymptotic limits of viscous Cahn-Hilliard equation with homogeneous Dirichlet boundary condition
- On the Cahn-Hilliard equation with irregular potentials and dynamic boundary conditions
- On the Cahn-Hilliard equation
- Compact sets in the space \(L^ p(0,T;B)\)
- A doubly nonlinear Cahn-Hilliard system with nonlinear viscosity
- An energetic variational approach for the Cahn-Hilliard equation with dynamic boundary condition: model derivation and mathematical analysis
- Existence and uniqueness of solutions to singular Cahn-Hilliard equations with nonlinear viscosity terms and dynamic boundary conditions
- Subdifferential operator approach to the Cahn-Hilliard equation with constraint
- Global solution to the Allen-Cahn equation with singular potentials and dynamic boundary conditions
- Convergence to the Poisson kernel for the Laplace equation with a nonlinear dynamical boundary condition
- A parabolic-elliptic chemotaxis system with nonlinear diffusion approached from a Cahn-Hilliard-type system
- The stochastic viscous Cahn-Hilliard equation: well-posedness, regularity and vanishing viscosity limit
- Numerical approximations and error analysis of the Cahn-Hilliard equation with dynamic boundary conditions
- Bounded solutions and their asymptotics for a doubly nonlinear Cahn-Hilliard system
- Long-time behavior of the Cahn-Hilliard equation with dynamic boundary condition
- The large diffusion limit for the heat equation in the exterior of the unit ball with a dynamical boundary condition
- Vanishing diffusion in a dynamic boundary condition for the Cahn-Hilliard equation
- Cahn-Hilliard equation on the boundary with bulk condition of Allen-Cahn type
- The Cahn-Hilliard equation and some of its variants
- Conditional stability in a backward Cahn-Hilliard equation via a Carleman estimate
- Convergence of Cahn–Hilliard systems to the Stefan problem with dynamic boundary conditions
- From the viscous Cahn–Hilliard equation to a regularized forward-backward parabolic equation
- Conditional stability in a backward parabolic system
- A Well Posed Problem for the Backward Heat Equation
- A Cahn–Hilliard model in bounded domains with permeable walls
- Robust exponential attractors for Cahn‐Hilliard type equations with singular potentials
- Nonlinear diffusion equations as asymptotic limits of Cahn‐Hilliard systems on unbounded domains via Cauchy's criterion
- Phase-field dynamics with transfer of materials: The Cahn–Hilliard equation with reaction rate dependent dynamic boundary conditions
- A direct approach to quasilinear parabolic equations on unbounded domains by Br\'ezis's theory for subdifferential operators
- The Cahn--Hilliard Equation with Forward-Backward Dynamic Boundary Condition via Vanishing Viscosity
- An Efficient and Convergent Finite Element Scheme for Cahn--Hilliard Equations with Dynamic Boundary Conditions
- The Cahn–Hilliard Equation: Recent Advances and Applications
- Weak Solutions of the Cahn--Hilliard System with Dynamic Boundary Conditions: A Gradient Flow Approach
- Free Energy of a Nonuniform System. I. Interfacial Free Energy
- Nonlinear Differential Equations of Monotone Types in Banach Spaces
- Boundary Integral Equations
- Nonlinear diffusion equations as asymptotic limits of Cahn-Hilliard systems
- On a transmission problem for equation and dynamic boundary condition of Cahn–Hilliard type with nonsmooth potentials