On a generalized Cahn-Hilliard equation with biological applications

By Laurence Cherfils, Alain Miranville, Sergey Zelik. 2014

113 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/958a6bb9ef95679b504487b28e4f743bc105ad7c

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In Applied Mathematics

In Computational Theory and Mathematics

In Materials Chemistry

Citations in the corpus

A Review on the Cahn-Hilliard Equation: Classical Results and Recent Advances in Dynamic Boundary Conditions (2021, background): “…fields and turned out to be e ffi cient tools for the study of a wide variety of segregation-like phenomena [8], for instance, diblock copolymer [9], image inpainting [10, 11], tumor growth [12, 13], biology [14], two-phase flows [7, 15–18], moving contact line dynamics [19, 20], and so on.”
The nonlocal Cahn–Hilliard equation with singular potential: Well-posedness, regularity and strict separation property (2017, methodology): “Afterwards, the Cahn– Hilliard equation and its variants has been used to model different phenomena which are characterized by segregation-like processes (see, for instance, [10, 26, 46, 48, 49, 54, 58, 59]).”