Affiliation:
1. Faculté des Sciences et Techniques, Université Marien Ngouabi, B.P. 69, Brazzaville, Congo
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.
Reference17 articles.
1. Long-time stabilization of solutions to a phase-field model with memory;Aizicovici;Journal of Evolution Equations,2001
2. Long-time convergence of solutions to a phase-field system;Aizicovici;Mathematical Methods in the Applied Sciences,2001
3. Mathematical study of multi-phase flow under shear through order parameter formulation;Boyer;Asymptot. Anal.,1999
4. Finite dimensional exponential attractors for the phase-field model;Brochet;Applied Analysis,1993
5. Conserved-phase field system; implication for kinetic undercooling;Cagilnalp;Appl. Rev-B,1988