Display Abstract

Title On a generalized Cahn-Hilliard equation with biological applications

Name Laurence Cherfils
Country France
Email laurence.cherfils@univ-lr.fr
Co-Author(s) A. Miranville, S. Zelik
Submit Time 2014-02-20 04:14:05
Special Session 2: Nonlinear evolution PDEs and interfaces in applied sciences
We will discuss the asymptotic behavior of a generalization of the Cahn-Hilliard equation with a proliferation term and endowed with Neumann boundary conditions. Such a model has, in particular, applications in biology. We show that either the average of the local density of cells is bounded, in which case we have a global in time solution, or the solution blows up in finite time. We will also prove that the relevant, from a biological point of view, solutions converge to 1 as time goes to infinity. We will end with some numerical simulations which confirm the theoretical results.