Computer-assisted equilibrium validation for the diblock copolymer model

60. Thomas Wanner:
    Computer-assisted equilibrium validation for the diblock copolymer model
    Discrete and Continuous Dynamical Systems, Series A 37(2), pp. 1075-1107, 2017.

Abstract

The diblock copolymer model is a fourth-order parabolic partial differential equation which models phase separation with fine structure. The equation is a gradient flow with respect to an extension of the standard van der Waals free energy functional which involves nonlocal interactions. Thus, the long-term dynamical behavior of the diblock copolymer model is described by its finite-dimensional attractor. However, even on one-dimensional domains, the full structure of the underlying equilibrium set is not fully understood. In this paper, we develop a rigorous computational approach for establishing the existence of equilibrium solutions of the diblock copolymer model. We consider both individual solutions, as well as pieces of solution branches in a parameter-dependent situation. The results are presented for the case of one-dimensional domains, and can easily be implemented using standard interval arithmetic packages.

Links

The published version of the paper can be found at https://doi.org/10.3934/dcds.2017045.

Bibtex

@article{wanner:17a,
   author = {Thomas Wanner},
   title = {Computer-assisted equilibrium validation for the
            diblock copolymer model},
   journal = {Discrete and Continuous Dynamical Systems, Series A},
   volume = {37},
   number = {2},
   year = {2017},
   pages = {1075--1107},
   doi = {10.3934/dcds.2017045}
   }