English

A doubly nonlinear Cahn-Hilliard system with nonlinear viscosity

Analysis of PDEs 2018-10-03 v2

Abstract

In this paper we discuss a family of viscous Cahn-Hilliard equations with a non-smooth viscosity term. This system may be viewed as an approximation of a "forward-backward" parabolic equation. The resulting problem is highly nonlinear, coupling in the same equation two nonlinearities with the diffusion term. In particular, we prove existence of solutions for the related initial and boundary value problem. Under suitable assumptions, we also state uniqueness and continuous dependence on data.

Keywords

Cite

@article{arxiv.1710.06698,
  title  = {A doubly nonlinear Cahn-Hilliard system with nonlinear viscosity},
  author = {Elena Bonetti and Pierluigi Colli and Luca Scarpa and Giuseppe Tomassetti},
  journal= {arXiv preprint arXiv:1710.06698},
  year   = {2018}
}

Comments

Key words and phrases: diffusion of species; Cahn-Hilliard equations; viscosity; non-smooth regularization; nonlinearities; initial-boundary value problem; existence of solutions; continuous dependence

R2 v1 2026-06-22T22:18:02.933Z