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Degenerate nonlocal Cahn-Hilliard equations : Well-posedness, regularity and local asymptotics

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2020

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Davoli, Elisa
Ranetbauer, Helene
Scarpa, Luca

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https://doi.org/10.1016/j.anihpc.2019.10.002
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http://arxiv.org/abs/1902.04469v2

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Annales de l'Institut Henri Poincaré (C) : Non Linear Analysis. Elsevier. 2020, 37(3), pp. 627-651. ISSN 0294-1449. eISSN 1873-1430. Available under: doi: 10.1016/j.anihpc.2019.10.002

Zusammenfassung

Existence and uniqueness of solutions for nonlocal Cahn-Hilliard equations with degenerate potential is shown. The nonlocality is described by means of a symmetric singular kernel not falling within the framework of any previous existence theory. A convection term is also taken into account. Building upon this novel existence result, we prove convergence of solutions for this class of nonlocal Cahn-Hilliard equations to their local counterparts, as the nonlocal convolution kernels approximate a Dirac delta. Eventually, we show that, under suitable assumptions on the data, the solutions to the nonlocal Cahn-Hilliard equations exhibit further regularity, and the nonlocal-to-local convergence is verified in a stronger topology.

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Fachgebiet (DDC)
510 Mathematik

Schlagwörter

Nonlocal Cahn-Hilliard equation, Degenerate potential, Singular kernel, Well-posedness, Nonlocal-to-local convergence, Convection

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ISO 690DAVOLI, Elisa, Helene RANETBAUER, Luca SCARPA, Lara TRUSSARDI, 2020. Degenerate nonlocal Cahn-Hilliard equations : Well-posedness, regularity and local asymptotics. In: Annales de l'Institut Henri Poincaré (C) : Non Linear Analysis. Elsevier. 2020, 37(3), pp. 627-651. ISSN 0294-1449. eISSN 1873-1430. Available under: doi: 10.1016/j.anihpc.2019.10.002
BibTex
@article{Davoli2020Degen-55542,
  year={2020},
  doi={10.1016/j.anihpc.2019.10.002},
  title={Degenerate nonlocal Cahn-Hilliard equations : Well-posedness, regularity and local asymptotics},
  number={3},
  volume={37},
  issn={0294-1449},
  journal={Annales de l'Institut Henri Poincaré (C) : Non Linear Analysis},
  pages={627--651},
  author={Davoli, Elisa and Ranetbauer, Helene and Scarpa, Luca and Trussardi, Lara}
}
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