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On the Cahn–Hilliard–Oono equation with singular potential and volume constraint

  • *Corresponding author: Giulio Schimperna

    *Corresponding author: Giulio Schimperna

This paper is dedicated to Pierluigi Colli sensei, on the occasion of his 65th birthday, with great admiration for his outstanding scientific work and even greater gratitude for everything he has taught us in many years

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  • We consider a new version of the Cahn–Hilliard–Oono equation with logarithmic potential of Flory–Huggins type, where we include a nonlocal constraint term acting on the spatial mean of the order parameter $ \varphi $ in order to force it remain inside the physical interval $ [-1,1] $ even in presence of an external mass source. By applying a modification of the methods that have been used to study the standard Cahn–Hilliard equation, it is then possible to discuss the existence and uniqueness of weak solutions and the regularity of solutions under appropriate assumptions. Applications of our results to tumor growth models are also detailed.

    Mathematics Subject Classification: Primary: 35D30, 35K35; Secondary: 35K86, 35Q92, 92C50.

    Citation:

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