Symmetry for Initial Boundary Value Problems of PDEs

@article{Jassim2019SymmetryFI,
  title={Symmetry for Initial Boundary Value Problems of PDEs},
  author={Aldhlki T. Jassim},
  journal={journal of the college of basic education},
  year={2019},
  volume={25},
  pages={178-194}
}
  • Aldhlki T. Jassim
  • Published 1 December 2019
  • Mathematics
  • journal of the college of basic education
Aldhlki T. Jassim Dep. of MathsCollege of Basic Education University of Mustansirya, Baghdad, Iraq talatjassim10@yahoo.com 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… 

References

SHOWING 1-10 OF 29 REFERENCES

Lie symmetries of nonlinear boundary value problems

The Blasius Function: Computations Before Computers, the Value of Tricks, Undergraduate Projects, and Open Research Problems

Although the Blasius flow solves a nonlinear partial differential equation (PDE), Toepfer successfully computed highly accurate numerical solutions in 1912, and it is shown that PDE numerical studies were possible even in the precomputer age.

Invariant boundary value problems for a fourth-order dynamic Euler-Bernoulli beam equation

We obtain the complete Lie symmetry group classification of the dynamic fourth-order Euler-Bernoulli partial differential equation, where the elastic modulus, the area moment of inertia are constants

Introduction to Symmetry Analysis

Preface 1. Introduction to symmetry 2. Dimensional analysis 3. Systems of ODE's, first order PDE's, state-space analysis 4. Classical dynamics 5. Introduction to one-parameter Lie groups 6. First

Boundary value problems for integrable equations compatible with the symmetry algebra

Boundary value problems for integrable nonlinear partial differential equations are considered from the symmetry point of view. Families of boundary conditions compatible with the Harry‐Dym, KdV, and

A new method for solving boundary value problems for partial differential equations

Similarity Analysis of Boundary Value Problems with Finite Boundaries

It is commonly believed that similarity analysis of boundary value problems in science and engineering is domain-and-boundary condition limited, in that semi-infinite or infinite domains are

Initial-value problems for evolutionary partial differential equations and higher-order conditional symmetries

We suggest a new approach to the problem of dimensional reduction of initial/ boundary value problems for evolution equations in one spatial variable. The approach is based on higher-order (general

Group analysis of ordinary differential equations and the invariance principle in mathematical physics (for the 150th anniversary of Sophus Lie)

CONTENTSPrefaceChapter I. Definitions and elementary applications §1.1. One-parameter transformation groups §1.2. Prolongation formulae §1.3. Groups admissible by differential equations §1.4.

Nonlinear boundary value problems on semi-infinite intervals