A geometrical formulation of the renormalization group method for global analysis II: Partial differential equations

1997 ◽  
Vol 14 (1) ◽  
pp. 51-69 ◽  
Author(s):  
Teiji Kunihiro
Keyword(s):  
Renormalization Group ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Global Analysis ◽  
Group Method ◽  
Renormalization Group Method ◽  
Partial Differential ◽  
Geometrical Formulation

scholarly journals Geometrical Formulation for Adjoint-Symmetries of Partial Differential Equations

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1547
Author(s):  
Stephen C. Anco ◽  
Bao Wang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Vector Fields ◽  
Evolution Equations ◽  
Applied Mathematics ◽  
Tangent Vector ◽  
Solution Space ◽  
Partial Differential ◽  
Geometrical Meaning ◽  
Geometrical Formulation

A geometrical formulation for adjoint-symmetries as one-forms is studied for general partial differential equations (PDEs), which provides a dual counterpart of the geometrical meaning of symmetries as tangent vector fields on the solution space of a PDE. Two applications of this formulation are presented. Additionally, for systems of evolution equations, adjoint-symmetries are shown to have another geometrical formulation given by one-forms that are invariant under the flow generated by the system on the solution space. This result is generalized to systems of evolution equations with spatial constraints, where adjoint-symmetry one-forms are shown to be invariant up to a functional multiplier of a normal one-form associated with the constraint equations. All of the results are applicable to the PDE systems of interest in applied mathematics and mathematical physics.

Lie Group Analysis for a Mixed Convective Flow and Heat Mass Transfer Over a Permeable Stretching Surface with Soret and Dufour Effects

2013 ◽  
Vol 30 (1) ◽  
pp. 67-75 ◽  
Author(s):  
Reda G. Abdel-Rahman ◽  
Ahmed M. Megahed
Keyword(s):  
Mass Transfer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Lie Group ◽  
Group Analysis ◽  
Group Method ◽  
Stretching Surface ◽  
Partial Differential ◽  
Soret And Dufour Effects

ABSTRACTThe Lie group transformation method is applied for solving the problem of mixed convection flow with mass transfer over a permeable stretching surface with Soret and Dufour effects. The application of Lie group method reduces the number of independent variables by one and consequently the system of governing partial differential equations reduces to a system of ordinary differential equations with appropriate boundary conditions. Further, the reduced non-linear ordinary differential equations are solved numerically by using the shooting method. The effects of various parameters governing the flow and heat transfer are shown through graphs and discussed. Our aim is to detect new similarity variables which transform our system of partial differential equations to a system of ordinary differential equations. In this work a special attention is given to investigate the effect of the Soret and Dufour numbers on the velocity, temperature and concentration fields above the sheet.

Numerical Renormalization Group Algorithms for Self-Similar Asymptotics of Partial Differential Equations

2020 ◽  
Vol 18 (1) ◽  
pp. 131-162
Author(s):  
Gasta͂o A. Braga ◽  
Frederico Furtado ◽  
Vincenzo Isaia ◽  
Long Lee
Keyword(s):  
Renormalization Group ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential ◽  
Numerical Renormalization Group ◽  
Self Similar

scholarly journals Renormalization group flow of a hierarchical Sine-Gordon model by partial differential equations

1991 ◽  
Vol 136 (2) ◽  
pp. 357-368 ◽  
Author(s):  
Thomas Kappeler ◽  
Klaus Pinn ◽  
Christian Wieczerkowski
Keyword(s):  
Renormalization Group ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Renormalization Group Flow ◽  
Partial Differential ◽  
Sine Gordon Model ◽  
Group Flow

scholarly journals Analysis of a renormalization group method and normal form theory for perturbed ordinary differential equations

2008 ◽  
Vol 237 (8) ◽  
pp. 1029-1052 ◽  
Author(s):  
R.E. Lee DeVille ◽  
Anthony Harkin ◽  
Matt Holzer ◽  
Krešimir Josić ◽  
Tasso J. Kaper
Keyword(s):  
Renormalization Group ◽  
Normal Form ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Group Method ◽  
Renormalization Group Method ◽  
Normal Form Theory ◽  
Form Theory
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