Symmetry for Initial Boundary Value Problems of PDEs

Abstract

In this paper, we discuss the reduction of IBVP by using the definition of Bluman or Ibragimov. Moreover, some examples that explain this definition for linear and nonlinear heat equation, are given. Next, we will give some restrictions on the Lie symmetry, which make the initial-boundary conditions are invariant. Finally, we find an initial condition which need not to be left invariant by a Lie symmetry in order to find an invariant solution, which satisfies that initial condition.