scholarly journals Variational problems within the class of solutions of a partial differential equation

1973 ◽  
Vol 180 ◽  
pp. 265-265
Author(s):  
Robert Delver
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Variational Problems ◽  
Partial Differential

An exact minimax penalty function approach to solve multitime variational problems

2020 ◽  
Vol 54 (3) ◽  
pp. 637-652 ◽  
Author(s):  
Anurag Jayswal ◽  
Preeti
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Variational Problem ◽  
Penalty Function ◽  
Function Method ◽  
Variational Problems ◽  
Penalty Function Method ◽  
Optimal Solutions ◽  
Partial Differential ◽  
Penalty Function Approach

This paper aims to examine an appropriateness of the exact minimax penalty function method applied to solve the partial differential inequation (PDI) and partial differential equation (PDE) constrained multitime variational problems. The criteria for equivalence between the optimal solutions of a multitime variational problem with PDI and PDE constraints and its associated unconstrained penalized multitime variational problem is studied in this work. We also present some examples to validate the results derived in the paper.

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.

Sign in / Sign up

Export Citation Format

Share Document