Lagrangian Approach to Evolution Equations: Symmetries and Conservation Laws

摘要

We present a Lagrangian approach to evolution equations by considering them together with their associated equations. The approach allows one to employ Noether's theorem and derive conservation laws from symmetries of the coupled system of evolution type equations. We apply our method to the linear and non-linear heat equations as well as to the Burgers equation and obtain new conservation laws using their symmetry Lie algebras.