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

Giuseppe Maria Coclite and Lorenzo di Ruvo
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Giuseppe Maria Coclite: Dipartimento di Meccanica, Matematica e Management, Politecnico di Bari, 70125 Bari, Italy
Lorenzo di Ruvo: Dipartimento di Matematica, Università di Bari, 70125 Bari, Italy

Mathematics, 2020, vol. 8, issue 10, 1-31

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.

Keywords: existence; uniqueness; stability; higher-order convective cahn-hilliard type equation; cauchy problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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