On the Cahn–Hilliard equation with dynamic boundary conditions and a dominating boundary potential

By Pierluigi Colli, Gianni Gilardi, Jürgen Sprekels. 2014

73 citations recorded by the source corpus.

The Cahn–Hilliard and viscous Cahn–Hilliard equations with singular and possibly nonsmooth potentials and dynamic boundary condition are considered and some well-posedness and regularity results are proved.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/cc06dc8b82cb645cfb96271ac9257d7d225594b2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Hao Wu
2. Pierluigi Colli
3. Takeshi Fukao
4. Jürgen Sprekels
5. Gianni Gilardi

In Computational Theory and Mathematics

1. Hao Wu
2. Pierluigi Colli
3. Takeshi Fukao
4. Jürgen Sprekels
5. Gianni Gilardi
6. David E. V. Rose

In Numerical Analysis

1. Hao Wu
2. Takeshi Fukao
3. Pierluigi Colli

Citations in the corpus

• Equation and dynamic boundary condition of Cahn-Hilliard type with singular potentials (2015, methodology): “These assumptions, in particular (A9), can be compared with the analogous ones in [12].”
• A Boundary Control Problem for the Viscous Cahn–Hilliard Equation with Dynamic Boundary Conditions (2014, background): “1 in [10] for the linear case reveals that the linear mapping, which assigns to each hΓ ∈ X the pair (ξ, ξΓ), where (ξ, ξΓ, η) is the associated unique solution to the linearized system (2.”
• A Review on the Cahn-Hilliard Equation: Classical Results and Recent Advances in Dynamic Boundary Conditions (2021, methodology): “For problem (3.9) with α ≥ 0 and some general assumptions on the potentials that cover all these typical cases (2.2), (2.3) and (2.4), the authors proved global existence, uniqueness and regularity results on its solutions (see [85, Theorem 2.2, Theorem 2.3, Theorem 2.4, Theorem 2.6]).”