Conservation laws for extended generalized Cahn–Hilliard–Kuramoto–Sivashinsky equation in any dimension

IF 1.7 3区化学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Journal of Mathematical Chemistry Pub Date : 2025-03-27 DOI:10.1007/s10910-025-01717-w

Pavel Holba

引用次数: 0

Abstract

We present a complete characterization of nontrivial local conservation laws for the extended generalized Cahn–Hilliard–Kuramoto–Sivashinsky equation in any space dimension. This equation naturally generalizes the well-known and widely used Cahn–Hilliard and Kuramoto–Sivashinsky equations, which have manifold applications in chemistry, physics, and biology. In particular, we demonstrate that any nontrivial local conservation law of any order for the equation under study is equivalent to a conservation law whose density is linear in the dependent variable with the coefficient at the dependent variable depending at most on the independent variables.

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任意维扩展广义Cahn-Hilliard-Kuramoto-Sivashinsky方程的守恒律

本文给出了任意空间维扩展广义Cahn-Hilliard-Kuramoto-Sivashinsky方程非平凡局部守恒律的完整刻画。这个方程自然地推广了著名的和广泛使用的Cahn-Hilliard方程和Kuramoto-Sivashinsky方程，这些方程在化学、物理和生物学中有多种应用。特别地，我们证明了所研究的方程的任何阶的非平凡局部守恒定律等价于密度在因变量上是线性的，而在因变量上的系数最多依赖于自变量的守恒定律。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Mathematical Chemistry 化学-化学综合

CiteScore

3.70

自引率

17.60%

发文量

105

审稿时长

6 months

期刊介绍： The Journal of Mathematical Chemistry (JOMC) publishes original, chemically important mathematical results which use non-routine mathematical methodologies often unfamiliar to the usual audience of mainstream experimental and theoretical chemistry journals. Furthermore JOMC publishes papers on novel applications of more familiar mathematical techniques and analyses of chemical problems which indicate the need for new mathematical approaches. Mathematical chemistry is a truly interdisciplinary subject, a field of rapidly growing importance. As chemistry becomes more and more amenable to mathematically rigorous study, it is likely that chemistry will also become an alert and demanding consumer of new mathematical results. The level of complexity of chemical problems is often very high, and modeling molecular behaviour and chemical reactions does require new mathematical approaches. Chemistry is witnessing an important shift in emphasis: simplistic models are no longer satisfactory, and more detailed mathematical understanding of complex chemical properties and phenomena are required. From theoretical chemistry and quantum chemistry to applied fields such as molecular modeling, drug design, molecular engineering, and the development of supramolecular structures, mathematical chemistry is an important discipline providing both explanations and predictions. JOMC has an important role in advancing chemistry to an era of detailed understanding of molecules and reactions.