On a Partial Differential Equation with Piecewise Constant Mixed Arguments

2020 ◽  
Vol 44 (6) ◽  
pp. 1791-1801
Author(s):  
Mehtap Lafci Büyükkahraman ◽  
Hüseyin Bereketoglu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential ◽  
Piecewise Constant ◽  
Mixed Arguments

scholarly journals A parabolic differential equation with unbounded piecewise constant delay

1992 ◽  
Vol 15 (2) ◽  
pp. 339-346 ◽  
Author(s):  
Joseph Wiener ◽  
Lokenath Debnath
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Difference Equations ◽  
Infinite Delay ◽  
Parabolic Differential Equation ◽  
Constant Delay ◽  
Partial Differential ◽  
Piecewise Constant ◽  
Greatest Integer Function

A partial differential equation with the argument[λt]is studied, where[•]denotes the greatest integer function. The infinite delayt−[λt]leads to difference equations of unbounded order.

scholarly journals Behavior of the solutions of a partial differential equation with a piecewise constant argument

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 5931-5943 ◽  
Author(s):  
Huseyin Bereketoglu ◽  
Mehtap Lafci
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Existence And Uniqueness ◽  
Partial Differential ◽  
Piecewise Constant ◽  
Piecewise Constant Argument ◽  
Oscillation Instability ◽  
Constant Argument

In this paper, we consider a partial differential equation with a piecewise constant argument. We study existence and uniqueness of the solutions of this equation. We also investigate oscillation, instability and stability of the solutions.

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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