scholarly journals Algebraic aspects of evolution partial differential equation arising in the study of constant elasticity of variance model from financial mathematics

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 31-36 ◽  
Author(s):  
Tanki Motsepa ◽  
Taha Aziz ◽  
Aeeman Fatima ◽  
Chaudry Masood Khalique
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Conservation Laws ◽  
General Theorem ◽  
Group Analysis ◽  
Partial Differential ◽  
Cev Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Evolution Partial Differential Equation

AbstractThe optimal investment-consumption problem under the constant elasticity of variance (CEV) model is investigated from the perspective of Lie group analysis. The Lie symmetry group of the evolution partial differential equation describing the CEV model is derived. The Lie point symmetries are then used to obtain an exact solution of the governing model satisfying a standard terminal condition. Finally, we construct conservation laws of the underlying equation using the general theorem on conservation laws.

scholarly journals Permeability Models for Magma Flow through the Earth's Mantle: A Lie Group Analysis

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
N. Mindu ◽  
D. P. Mason
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Volume Fraction ◽  
Solitary Wave Solution ◽  
Nonlinear Partial Differential Equation ◽  
Group Analysis ◽  
Partial Differential ◽  
Magma Flow ◽  
Exponential Law ◽  
Flow Through

The migration of melt through the mantle of the Earth is governed by a third-order nonlinear partial differential equation for the voidage or volume fraction of melt. The partial differential equation depends on the permeability of the medium which is assumed to be a function of the voidage. It is shown that the partial differential equation admits, as well as translations in time and space, other Lie point symmetries provided the permeability is either a power law or an exponential law of the voidage or is a constant. A rarefactive solitary wave solution of the partial differential equation is derived in the form of a quadrature for the exponential law for the permeability.

Group Theoretical Analysis and Invariant Solutions for Unsteady Flow of a Fourth-Grade Fluid over an Infinite Plate Undergoing Impulsive Motion in a Darcy Porous Medium

2015 ◽  
Vol 70 (7) ◽  
pp. 483-497 ◽  
Author(s):  
Taha Aziz ◽  
Aeeman Fatima ◽  
Asim Aziz ◽  
Fazal M. Mahomed
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Lie Group ◽  
Group Analysis ◽  
Fourth Grade ◽  
Invariant Solutions ◽  
Conditional Symmetry ◽  
Partial Differential ◽  
Grade Fluid ◽  
Fourth Grade Fluid

AbstractIn this study, an incompressible time-dependent flow of a fourth-grade fluid in a porous half space is investigated. The flow is generated due to the motion of the flat rigid plate in its own plane with an impulsive velocity. The partial differential equation governing the motion is reduced to ordinary differential equations by means of the Lie group theoretic analysis. A complete group analysis is performed for the governing nonlinear partial differential equation to deduce all possible Lie point symmetries. One-dimensional optimal systems of subalgebras are also obtained, which give all possibilities for classifying meaningful solutions in using the Lie group analysis. The conditional symmetry approach is also utilised to solve the governing model. Various new classes of group-invariant solutions are developed for the model problem. Travelling wave solutions, steady-state solution, and conditional symmetry solutions are obtained as closed-form exponential functions. The influence of pertinent parameters on the fluid motion is graphically underlined and discussed.

scholarly journals Symmetry Analysis and Conservation Laws of a Generalization of the Kelvin-Voigt Viscoelasticity Equation

Symmetry ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 840 ◽  
Author(s):  
Almudena P. Márquez ◽  
María S. Bruzón
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Partial Differential Equation ◽  
Conservation Laws ◽  
Mechanical Behaviour ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Point Symmetries ◽  
Lie Symmetry Analysis ◽  
Partial Differential

In this paper, we study a generalization of the well-known Kelvin-Voigt viscoelasticity equation describing the mechanical behaviour of viscoelasticity. We perform a Lie symmetry analysis. Hence, we obtain the Lie point symmetries of the equation, allowing us to transform the partial differential equation into an ordinary differential equation by using the symmetry reductions. Furthermore, we determine the conservation laws of this equation by applying the multiplier method.

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