Abstract
Last time symmetry methods have been recognized to be of great importance for the study of the differential equations arising in mathematics and physics. The purpose of this paper is to provide some application of Lie groups to heat equation. In this example, we determine Lie algebra of infinitesimal generators of symmetry group of heat equation and construct group-invariant solutions of this equation. The some computational methods are presented so that researchers in other fields can readily learn to use them.
Highlights
Suppose we are given differential equation of order m ( ) ∆ x,u(m) = 0 (1)from n independent of x = ( x1, x2, xn ) and q dependent variables ( ) =u u1,u2,uq ∈ RqDefinition
Last time symmetry methods have been recognized to be of great importance for the study of the differential equations arising in mathematics and physics
A group G of transformation acting on an open subset M of the space of independent and dependent variables X × Rq, is called the symmetry group of Equation (1) if for each solution u = f ( x) of Equation (1) and for g ∈G such that g f is defined, the function u = g f is a solution of the equation
Summary
How to cite this paper: Abdigapparovich, N.O. (2018) Lie Algebra of Infinitesimal Generators of the Symmetry Group of the Heat Equation. How to cite this paper: Abdigapparovich, N.O. (2018) Lie Algebra of Infinitesimal Generators of the Symmetry Group of the Heat Equation. Journal of Applied Mathematics and Physics, 6, 373-381. Received: October 6, 2017 Accepted: February 11, 2018 Published: February 14, 2018
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
