Long-time existence of classical solutions to a one-dimensional swelling gel

M. Carme Calderer, Robin Ming Chen

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

In this paper, we derived a model which describes the swelling dynamics of a gel and study the system in one-dimensional geometry with a free boundary. The governing equations are hyperbolic with a weakly dissipative source. Using a mass-Lagrangian formulation, the free boundary is transformed into a fixed boundary. We prove the existence of long-time C1-solutions to the transformed fixed boundary problem.

Original languageEnglish (US)
Pages (from-to)165-194
Number of pages30
JournalMathematical Models and Methods in Applied Sciences
Volume25
Issue number1
DOIs
StatePublished - Jan 1 2015

Keywords

  • Flory-Huggins mixing energy
  • Gel-swelling
  • continuum model
  • dissipative mechanisms
  • hyperbolic free boundary problem

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