[图书][B] The Cahn–Hilliard equation: recent advances and applications
A Miranville - 2019 - SIAM
This book discusses classical results, as well as recent developments, related to the Cahn–
Hilliard equation. It is based on the lectures that I gave at the CBMS-NSF Conference on the …
Hilliard equation. It is based on the lectures that I gave at the CBMS-NSF Conference on the …
Generalized SAV-exponential integrator schemes for Allen--Cahn type gradient flows
The energy dissipation law and the maximum bound principle (MBP) are two important
physical features of the well-known Allen--Cahn equation. While some commonly used first …
physical features of the well-known Allen--Cahn equation. While some commonly used first …
A positivity-preserving, energy stable scheme for a ternary Cahn-Hilliard system with the singular interfacial parameters
In this paper, we construct and analyze a uniquely solvable, positivity preserving and
unconditionally energy stable finite-difference scheme for the periodic three-component …
unconditionally energy stable finite-difference scheme for the periodic three-component …
A positivity-preserving, energy stable and convergent numerical scheme for the Poisson-Nernst-Planck system
In this paper we propose and analyze a finite difference numerical scheme for the Poisson-
Nernst-Planck equation (PNP) system. To understand the energy structure of the PNP …
Nernst-Planck equation (PNP) system. To understand the energy structure of the PNP …
Unconditionally maximum bound principle preserving linear schemes for the conservative Allen–Cahn equation with nonlocal constraint
In comparison with the Cahn–Hilliard equation, the classic Allen-Cahn equation satisfies the
maximum bound principle (MBP) but fails to conserve the mass along the time. In this paper …
maximum bound principle (MBP) but fails to conserve the mass along the time. In this paper …
A structure-preserving, operator splitting scheme for reaction-diffusion equations with detailed balance
In this paper, we propose and analyze a positivity-preserving, energy stable numerical
scheme for a certain type of reaction-diffusion systems involving the Law of Mass Action with …
scheme for a certain type of reaction-diffusion systems involving the Law of Mass Action with …
Stabilized integrating factor Runge--Kutta method and unconditional preservation of maximum bound principle
The maximum bound principle (MBP) is an important property for a large class of semilinear
parabolic equations, in the sense that the time-dependent solution of the equation with …
parabolic equations, in the sense that the time-dependent solution of the equation with …
[HTML][HTML] Continuum-scale modelling of polymer blends using the Cahn–Hilliard equation: transport and thermodynamics
The Cahn–Hilliard equation is commonly used to study multi-component soft systems such
as polymer blends at continuum scales. We first systematically explore various features of …
as polymer blends at continuum scales. We first systematically explore various features of …
Uniqueness and regularity for the Navier--Stokes--Cahn--Hilliard system
The motion of two contiguous incompressible and viscous fluids is described within the
diffuse interface theory by the so-called Model H. The system consists of the Navier--Stokes …
diffuse interface theory by the so-called Model H. The system consists of the Navier--Stokes …
Linear energy stable and maximum principle preserving semi-implicit scheme for Allen–Cahn equation with double well potential
X Wang, J Kou, H Gao - … in Nonlinear Science and Numerical Simulation, 2021 - Elsevier
In this paper, we consider numerical approximation of the Allen–Cahn equation with double
well potential, which is a fundamental equation in phase-field models. We propose a novel …
well potential, which is a fundamental equation in phase-field models. We propose a novel …