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On a generalized Cahn-Hilliard equation with biological applications

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  • In this paper, we are interested in the study of 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 further prove that the relevant, from a biological point of view, solutions converge to $1$ as time goes to infinity. We finally give some numerical simulations which confirm the theoretical results.
    Mathematics Subject Classification: 35B40, 35B44, 35K55.

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