Structure-preserving finite difference schemes for the Cahn-Hilliard equation with dynamic boundary conditions in the one-dimensional case
| Autor: | Saori Wada, Takeshi Fukao, Shuji Yoshikawa |
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| Rok vydání: | 2017 |
| Předmět: |
Partial differential equation
Applied Mathematics 010102 general mathematics Mathematical analysis General Medicine Mixed boundary condition 01 natural sciences Poincaré–Steklov operator Robin boundary condition 010101 applied mathematics Boundary conditions in CFD Neumann boundary condition Free boundary problem Boundary value problem 0101 mathematics Analysis Mathematics |
| Zdroj: | Communications on Pure & Applied Analysis. 16:1915-1938 |
| ISSN: | 1553-5258 |
| Popis: | The structure-preserving finite difference schemes for the one dimensional Cahn-Hilliard equation with dynamic boundary conditions are studied. A dynamic boundary condition is a sort of transmission condition that includes the time derivative, namely, it is itself a time evolution equation. The Cahn-Hilliard equation with dynamic boundary conditions is well-treated from various viewpoints. The standard type consists of a dynamic boundary condition for the order parameter, and the Neumann boundary condition for the chemical potential. Recently, Goldstein-Miranville-Schimperna proposed a new type of dynamic boundary condition for the Cahn-Hilliard equation. In this article, numerical schemes for the problem with these two kinds of dynamic boundary conditions are introduced. In addition, a mathematical result on the existence of a solution for the scheme with an error estimate is also obtained for the former boundary condition. |
| Databáze: | OpenAIRE |
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