| dc.description.abstract | Burgers equation: u, + UUx = luxx is a nonlinear partial differential equation which arises
in model studies of turbulence and shock wave theory. In physical application of shock
waves in fluids, coefficient 1 ,has the meaning of viscosity. For light fluids or gases the
solution considers the inviscid limit as 1 tends to zero. The solution of Burgers equation
can be classified into two categories: Numerical solutions using both finite difference and
finite elements approaches; the analytic solutions found by Cole and Hopf In both cases
the solutions have been valid for only 0 ~ 1 ~ 1. In this thesis, we have found a global
solution to the Burgers equation with no restriction on 1 i.e. 1 E (- 00 , 00). In pursuit
of our objective, we have used, the Lie symmetry analysis. The method includes the
development of infinitesimal transformations, generators, prolongations, and the invariant
transformations of the Burgers equation. We have managed to determine all the Lie
groups admitted by the Burgers equation, and used the symmetry transformations to
establish all the solutions corresponding to each Lie group admitted by the equation.
These solutions, which are appearing in literature for the first time are more explicit and
more general than those previously obtained. This is a big contribution to the
mathematical knowledge in the application of Burgers equation. | en_US |
