Cahn-Hilliard-Oono方程在三维空间中的适定性
Well-Posedness of the Cahn-Hilliard-Oono Equation in Three-Dimensional Space
DOI: 10.12677/AAM.2020.99191, PDF,   
作者: 段 芳, 蒲志林, 黄 梅：四川师范大学数学科学学院，四川 成都
关键词: Cahn-Hilliard方程；无界区域；整体适定性；Cahn-Hilliard Equation； Unbounded Domains； Global Well-Posedness
摘要: 考虑Cahn-Hilliard-Oono方程在三维空间中的柯西问题。通过对经典方程添加βu项(β>0)，更好的分析系统的长程相互作用，首先证明了方程在H1(R3)上是局部可解的，进一步得到解的整体适定性和解半群的耗散性。
Abstract: The Cauchy problem of Cahn-Hilliard-Oono in three-dimensional space is considered. By adding a term βu to the classical equation, we can better analyze the long-range interaction of the system. Firstly, it is proved that the equation is locally solvable on H1(R3), and then the global well posedness of the solution and the dissipation of the semigroup are obtained.
文章引用：段芳, 蒲志林, 黄梅. Cahn-Hilliard-Oono方程在三维空间中的适定性[J]. 应用数学进展, 2020, 9(9): 1645-1651. https://doi.org/10.12677/AAM.2020.99191

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