Multidimensional partial differential equation systems: Generating new systems via conservation laws, potentials, gauges, subsystems

2010 ◽  
Vol 51 (10) ◽  
pp. 103521 ◽  
Author(s):  
Alexei F. Cheviakov ◽  
George W. Bluman
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Conservation Laws ◽  
Partial Differential

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 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.

Qxygen transfer in gravity flow sewers

2000 ◽  
Vol 42 (3-4) ◽  
pp. 417-422 ◽  
Author(s):  
T.Y. Pai ◽  
C.F. Ouyang ◽  
Y.C. Liao ◽  
H.G. Leu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dissolved Oxygen ◽  
Flow Velocity ◽  
Molecular Diffusion ◽  
Eddy Diffusion ◽  
Partial Differential ◽  
Diffusion Term ◽  
Sewer Pipes ◽  
Gravity Sewer

Oxygen diffused to water in gravity sewer pipes was studied in a 21 m long, 0.15 m diameter model sewer. At first, the sodium sulfide was added into the clean water to deoxygenate, then the pump was started to recirculate the water and the deoxygenated water was reaerated. The dissolved oxygen microelectrode was installed to measure the dissolved oxygen concentrations varied with flow velocity, time and depth. The dissolved oxygen concentration profiles were constructed and observed. The partial differential equation diffusion model that considered Fick's law including the molecular diffusion term and eddy diffusion term were derived. The analytic solution of the partial differential equation was used to determine the diffusivities by the method of nonlinear regression. The diffusivity values for the oxygen transfer was found to be a function of molecular diffusion, eddy diffusion and flow velocity.

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