论文标题
带有交叉扩散的反应扩散系统：谎言对称性，精确的解决方案及其在大流行建模中的应用
A reaction-diffusion system with cross-diffusion: Lie symmetry, exact solutions and their applications in the pandemic modeling
论文作者
论文摘要
使用Lie Symmetry方法研究了具有描述COVID-19爆发的交叉扩散系统的非线性反应扩散系统。得出了一个完整的谎言对称分类，并表明具有正确指定参数的系统允许高度非平凡的谎言对称性算子，这对于所有已知的反应扩散系统并非发生。从适用性的角度来看，在最有趣的情况下，获得的对称性也用于查找系统的精确解。结果表明，得出的确切溶液具有描述在空间1d近似下的大流行扩散并导致分布的所有必要属性，该分布与乌克兰的Covid-19的测量数据相对应。
A nonlinear reaction-diffusion system with cross-diffusion describing the COVID-19 outbreak is studied using the Lie symmetry method. A complete Lie symmetry classification is derived and it is shown that the system with correctly-specified parameters admits highly nontrivial Lie symmetry operators, which do not occur for all known reaction-diffusion systems. The symmetries obtained are also applied for finding exact solutions of the system in the most interesting case from applicability point of view. It is shown that the exact solutions derived possess all necessary properties for describing the pandemic spread under 1D approximation in space and lead to the distributions, which qualitatively correspond to the measured data of the COVID-19 spread in Ukraine.
