On the Existence of Strong Solutions to the Cahn--Hilliard--Darcy System with Mass Source

Andrea Giorgini, Kei Fong Lam, Elisabetta Rocca, Giulio Schimperna

Research output: Contribution to journalArticlepeer-review

Abstract

We study a diffuse interface model describing the evolution of the flow of a binary fluid in a Hele-Shaw cell. The model consists of a Cahn--Hilliard--Darcy type system with transport and mass source. A relevant physical application is related to tumor growth dynamics, which in particular justifies the occurrence of a mass inflow. We study the initial-boundary value problem for this model and prove global existence and uniqueness of strong solutions in two space dimensions as well as local existence in three space dimensions.

Original languageEnglish
Pages (from-to)737-767
Number of pages31
JournalSIAM Journal on Mathematical Analysis
Volume54
Issue number1
DOIs
Publication statusPublished - Jan 2022

Scopus Subject Areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Cahn-Hilliard-Darcy system
  • logarithmic potentials
  • nonlinear evolutionary system
  • strong solutions
  • well-posedness

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