A physics informed neural network (PINN) incorporates the physics of a system by satisfying
its boundary value problem through a neural network's loss function. The PINN approach …

The Cahn-Hilliard equation is a fundamental model that describes the phase separation
process in multi-component mixtures. It has been successfully extended to many different …

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 …

Abstract The Cahn–Hilliard equation is a fundamental model that describes phase
separation processes of binary mixtures. In recent years, several types of dynamic boundary …

In this paper, we propose and analyze a second order accurate in time, mass lumped mixed
finite element scheme for the Cahn-Hilliard equation with a logarithmic Flory-Huggins …

We consider the problem of the long time dynamics for a diffuse interface model for tumor
growth. The model describes the growth of a tumor surrounded by host tissues in the …

In this study, the direct meshless local Petrov–Galerkin (DMLPG) method has been
employed to solve the stochastic Cahn–Hilliard–Cook and Swift–Hohenberg equations. First …

We propose a new type of diffuse interface model describing the evolution of a tumor mass
under the effects of a chemical substance (eg, a nutrient or a drug). The process is described …

We present a structure preserving PINN for solving a series of time dependent PDEs with
periodic boundary. Our method can incorporate the periodic boundary condition as the …

The design of numerical approximations of the Cahn-Hilliard model preserving the
maximum principle is a challenging problem, even more if considering additional transport …