کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1898662 | 1044753 | 2012 | 14 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Lie point symmetries of a general class of PDEs: The heat equation
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
فیزیک ریاضی
پیش نمایش صفحه اول مقاله
![عکس صفحه اول مقاله: Lie point symmetries of a general class of PDEs: The heat equation Lie point symmetries of a general class of PDEs: The heat equation](/preview/png/1898662.png)
چکیده انگلیسی
We give two theorems which show that the Lie point and the Noether symmetries of a second-order ordinary differential equation of the form DDs(Dxi(s)Ds)=F(xi(s),xÌj(s)) are subalgebras of the special projective and the homothetic algebra of the space respectively. We examine the possible extension of this result to partial differential equations (PDE) of the form AijuijâF(xi,u,ui)=0 where u(xi) and uij stands for the second partial derivative. We find that if the coefficients Aij are independent of u(xi) then the Lie point symmetries of the PDE form a subgroup of the conformal symmetries of the metric defined by the coefficients Aij. We specialize the study to linear forms of F(xi,u,ui) and write the Lie symmetry conditions for this case. We apply this result to two cases. The wave equation in an inhomogeneous medium for which we derive the Lie symmetry vectors and check our results with those in the literature. Subsequently we consider the heat equation with a flux in an nâdimensional Riemannian space and show that the Lie symmetry algebra is a subalgebra of the homothetic algebra of the space. We discuss this result in the case of de Sitter space time and in flat space.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Geometry and Physics - Volume 62, Issue 12, December 2012, Pages 2443-2456
Journal: Journal of Geometry and Physics - Volume 62, Issue 12, December 2012, Pages 2443-2456
نویسندگان
Andronikos Paliathanasis, Michael Tsamparlis,