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 …

In this survey article, a variety of systems modeling tumor growth are discussed. In
accordance with the hallmarks of cancer, the described models incorporate the primary …

This paper outlines a rigorous variational-based multilevel Global–Local formulation for
ductile fracture. Here, a phase-field formulation is used to resolve failure mechanisms by …

The prediction of crack initiation and propagation in ductile failure processes are
challenging tasks for the design and fabrication of metallic materials and structures on a …

This paper presents a novel variational phase-field model for different fracture processes in
fully saturated porous media. As a key feature, the model employs a micromechanics-based …

An element-free Galerkin (EFG) method is presented for the numerical solution of the
obstacle boundary value problem. To deal with the nonlinear inequality governing equations …

In this paper we propose a Nonlocal Operator Method (NOM) for the solution of the Cahn-
Hilliard (CH) equation exploiting the higher order continuity of the NOM. The method is …

In this article, we consider the Cahn–Hilliard–Brinkman–Ohta–Kawasaki tumor growth
system, which couples the Brinkman flow equations in the porous medium and the Cahn …

Most implicit methods for the Swift–Hohenberg (SH) equation with quadratic–cubic
nonlinearity require costly iterative solvers at each time step. In this paper, a non-iterative …

Recently developed phase field models of fracture require a diffusive crack representation
based on an introduction of a crack phase field. We outline a thermodynamically consistent …