论文标题
为时期热方程式的谎言代数和保护法
Lie Algebra and Conservation Laws for the Time-fractional Heat Equation
论文作者
论文摘要
使用Lie对称方法来得出N维分数热方程的点对称性。我们发现，与所有维度的非分类顺序相比，对称和谎言括号的数量显着减少。实际上，对于整数阶线性热方程，解决方案对称的数量等于订单和空间维度的乘积，而对于分数情况，它是订单和空间维度上乘积的一半。我们已经对对称性进行了分类，并讨论了Lie代数和保护法律。我们将对称性的数量推广到N维热方程。
The Lie symmetry method is applied to derive the point symmetries for the N-dimensional fractional heat equation. We find that that the numbers of symmetries and Lie brackets are reduced significantly as compared to the nonfractional order for all the dimensions. In fact for integer order linear heat equation the number of solution symmetries is equal to the product of the order and space dimension, whereas for the fractional case, it is half of the product on the order and space dimension. We have classified the symmetries and discussed the Lie algebras and conservational laws. We generalise the number of symmetries to the n-dimensional heat equation.
