具有容许例外李对称性的含对数非线性项的多维抛物方程
Multidimensional parabolic equations with a logarithmic nonlinearity admitting exceptional Lie symmetries
浏览论文内容
中文总结 AI 辅助
该研究针对具有对数非线性项的多维抛物方程，通过渐近方法和李对称分类，识别了非自治源项下的例外对称性，并构造了精确解。
中文摘要 AI 辅助
非线性反应-扩散方程在非常广泛的应用中出现。这里我们研究一个特定的多维类别，其中源项在时间上非自治，这一选择既源于其与一大类（自治的）“近线性”反应-扩散方程的相关性，也源于由此产生的异常丰富的李对称性（包括对任意时间依赖，以及出现四个更例外的情形）；前者通过标准渐近方法推导，后者则需要详细的李对称性分类。还注意到对常微分方程的李约化与非李约化，并构造了相关的精确解。
英文摘要
Nonlinear reaction-diffusion equations arise in a very wide range of applications. Here we address a specific multidimensional class in which the source term is non-autonomous in time, this choice being motivated both by its relevance to a broad class of (autonomous) `near-linear' reaction-diffusion equations and by the unusually rich nature of the Lie symmetries that results (including for arbitrary time-dependence, and with four even more exceptional cases arising). The class of non-autonomous equation analysed is derived by an asymptotic approach, with the Lie symmetry classification and a further analysis subsequently carried out. Both Lie and non-Lie reductions to ordinary differential equations are also noted and relevant exact solutions are constructed.
发表机构
- University of Nottingham（诺丁汉大学）
- National University of Kyiv-Mohyla Academy（基辅莫希拉学院）
机构由 AI 辅助整理，请以论文原文为准。
