A Note on the Solutions for a Higher-Order Convective Cahn–Hilliard-Type Equation
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 <inline-f...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-10-01
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| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/8/10/1835 |
| Summary: | 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 <inline-formula><math display="inline"><semantics><msup><mi>H</mi><mn>3</mn></msup></semantics></math></inline-formula> 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. |
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| ISSN: | 2227-7390 |