scholarly journals A Linear Homogeneous Partial Differential Equation with Entire Solutions Represented by Laguerre Polynomials

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Xin-Li Wang ◽  
Feng-Li Zhang ◽  
Pei-Chu Hu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Laguerre Polynomials ◽  
Convergent Series ◽  
Entire Solutions ◽  
Partial Differential ◽  
Order And Type

We study a homogeneous partial differential equation and get its entire solutions represented in convergent series of Laguerre polynomials. Moreover, the formulae of the order and type of the solutions are established.

scholarly journals On Generalized Growth of Analytic Functions Solutions of Linear Homogeneous Partial Differential Equation of Second Order

2017 ◽  
Vol 2017 ◽  
pp. 1-6
Author(s):  
Devendra Kumar
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential Equations ◽  
Analytic Functions ◽  
Growth Parameters ◽  
Laguerre Polynomials ◽  
Convergent Series ◽  
Second Order ◽  
Partial Differential ◽  
Generalized Type

The generalized growth parameters of analytic functions solutions of linear homogeneous partial differential equations of second order have been studied. Moreover, coefficients characterizations of generalized order and generalized type of the solutions represented in convergent series of Laguerre polynomials have been obtained.

Entire solutions of a variation of the eikonal equation and related PDEs

2020 ◽  
Vol 63 (3) ◽  
pp. 697-708
Author(s):  
Feng Lü
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Entire Function ◽  
Eikonal Equation ◽  
Entire Solutions ◽  
Partial Differential ◽  
Tubular Surfaces

AbstractThe aim of this paper is twofold. The first aim is to describe the entire solutions of the partial differential equation (PDE) $u_{z_1}^2+2Bu_{z_1}u_{z_2}+u_{z_2}^2=e^g$, where B is a constant and g is a polynomial or an entire function in $\mathbb {C}^2$. The second aim is to consider the entire solutions of another PDE, which is a generalization of the well-known PDE of tubular surfaces.

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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