论文标题
非线性四阶抛物线方程的熵划分有限差异方案
Entropy-dissipating finite-difference schemes for nonlinear fourth-order parabolic equations
论文作者
论文摘要
得出了一维圆环上一般非线性四阶方程的结构保留有限差异方案。示例包括薄膜和德里达 - lebowitz-sper-spohn方程。这些方案保存质量并消散熵。与对数熵相关的方案也保留了积极性。派生的想法是以避免链条规则的方式重新重新重新制定方程式。然后将中心有限差异化离散化应用于重新制定。这样，恢复了与连续情况相同的耗散率。该策略可以扩展到多维薄膜方程。一个和两个空间维度中的数值示例说明了耗散属性。
Structure-preserving finite-difference schemes for general nonlinear fourth-order parabolic equations on the one-dimensional torus are derived. Examples include the thin-film and the Derrida-Lebowitz-Speer-Spohn equations. The schemes conserve the mass and dissipate the entropy. The scheme associated to the logarithmic entropy also preserves the positivity. The idea of the derivation is to reformulate the equations in such a way that the chain rule is avoided. A central finite-difference discretization is then applied to the reformulation. In this way, the same dissipation rates as in the continuous case are recovered. The strategy can be extended to a multi-dimensional thin-film equation. Numerical examples in one and two space dimensions illustrate the dissipation properties.
