Cahn–Hilliard system with proliferation term

Article type: Research Article

Authors: Nimi, Aymard Christbert^{; *} | Langa, Franck Davhys Reval

Affiliations: Faculté des Sciences et Techniques, Université Marien Ngouabi, B.P. 69, Brazzaville, Congo

Correspondence: [*] Corresponding author. E-mail: nimichristbert@gmail.com.

Abstract: In this article, our objective is to explore a Cahn–Hilliard system with a proliferation term, particularly relevant in biological contexts, with Neumann boundary conditions. We commence our investigation by establishing the boundedness of the average values of the local cell density u and the temperature H. This observation suggests that the solution (u,H) either persists globally in time or experiences finite-time blow-up. Subsequently, we prove the convergence of u to 1 and H to 0 as time approaches infinity. Finally, we bolster our theoretical findings with numerical simulations.

Keywords: Cahn–Hilliard system, proliferation term, dissipativity, blow up, simulations

DOI: 10.3233/ASY-241915

Journal: Asymptotic Analysis, vol. 140, no. 1-2, pp. 123-145, 2024