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On the viscous Cahn-Hilliard equation with singular potential and inertial term

Dipartimento di Matematica, Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy

Special Issues: Nonlinear Evolution PDEs, Interfaces and Applications

We consider a relaxation of the viscous Cahn-Hilliard equation induced by the second-order inertial term utt. The equation also contains a semilinear term f(u) of “singular” type. Namely, the function f is defined only on a bounded interval of R corresponding to the physically admissible values of the unknown u, and diverges as u approaches the extrema of that interval. In view of its interaction with the inertial term utt, the term f(u) is diffcult to be treated mathematically. Based on an approach originally devised for the strongly damped wave equation, we propose a suitable concept of weak solution based on duality methods and prove an existence result.
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Keywords Cahn-Hilliard equation; inertia; weak formulation; maximal monotone operator; duality

Citation: Riccardo Scala, Giulio Schimperna. On the viscous Cahn-Hilliard equation with singular potential and inertial term. AIMS Mathematics, 2016, 1(1): 64-76. doi: 10.3934/Math.2016.1.64

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This article has been cited by

  • 1. Elena Bonetti, Elisabetta Rocca, Riccardo Scala, Giulio Schimperna, On the strongly damped wave equation with constraint, Communications in Partial Differential Equations, 2017, 1, 10.1080/03605302.2017.1345937
  • 2. Alain Miranville, The Cahn–Hilliard equation and some of its variants, AIMS Mathematics, 2017, 2, 3, 479, 10.3934/Math.2017.2.479
  • 3. Xiaofeng Yang, Jia Zhao, Xiaoming He, Linear, second order and unconditionally energy stable schemes for the viscous Cahn-Hilliard equation with hyperbolic relaxation using the invariant energy quadratization method, Journal of Computational and Applied Mathematics, 2018, 10.1016/j.cam.2018.04.027
  • 4. Zhenguo Mu, Yuezheng Gong, Wenjun Cai, Yushun Wang, Efficient local energy dissipation preserving algorithms for the Cahn–Hilliard equation, Journal of Computational Physics, 2018, 374, 654, 10.1016/j.jcp.2018.08.004

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