| Contents |
| 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. |
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