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A Note on the Solutions for a Higher-Order Convective Cahn–Hilliard-Type Equation

Author

Listed:
  • Giuseppe Maria Coclite

    (Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, 70125 Bari, Italy
    These authors contributed equally to this work.)

  • Lorenzo di Ruvo

    (Dipartimento di Matematica, Università di Bari, 70125 Bari, Italy
    These authors contributed equally to this work.)

Abstract

The higher-order convective Cahn-Hilliard equation describes the evolution of crystal surfaces faceting through surface electromigration, the growing surface faceting, and the evolution of dynamics of phase transitions in ternary oil-water-surfactant systems. In this paper, we study the H 3 solutions of the Cauchy problem and prove, under different assumptions on the constants appearing in the equation and on the mean of the initial datum, that they are well-posed.

Suggested Citation

  • Giuseppe Maria Coclite & Lorenzo di Ruvo, 2020. "A Note on the Solutions for a Higher-Order Convective Cahn–Hilliard-Type Equation," Mathematics, MDPI, vol. 8(10), pages 1-31, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1835-:d:431107
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    References listed on IDEAS

    as
    1. Giuseppe Maria Coclite & Lorenzo di Ruvo, 2018. "Convergence of the regularized short pulse equation to the short pulse one," Mathematische Nachrichten, Wiley Blackwell, vol. 291(5-6), pages 774-792, April.
    2. Aibo Liu & Changchun Liu, 2014. "Weak Solutions for a Sixth Order Cahn-Hilliard Type Equation with Degenerate Mobility," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, April.
    3. Zhao Wang & Changchun Liu, 2012. "Some Properties of Solutions for the Sixth-Order Cahn-Hilliard-Type Equation," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-24, October.
    Full references (including those not matched with items on IDEAS)

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