Weak Solutions of a Partial Differential Equation of Dynamic Programming

1971 ◽  
Vol 9 (4) ◽  
pp. 519-528 ◽  
Author(s):  
Raymond W. Rishel
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Dynamic Programming ◽  
Weak Solutions ◽  
Partial Differential

scholarly journals Asymptotic Behavior of Weak Solutions to the Generalized Nonlinear Partial Differential Equation Model

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
Min Wu ◽  
Yousheng Wu
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Asymptotic Behavior ◽  
Weak Solutions ◽  
Nonlinear Partial Differential Equation ◽  
Equation Model ◽  
Differential Equation Model ◽  
Partial Differential ◽  
Large Perturbation ◽  
Partial Differential Equation Model

This paper investigates the asymptotic behavior of weak solutions to the generalized nonlinear partial differential equation model. It is proved that every perturbed weak solution of the perturbed generalized nonlinear partial differential equations asymptotically converges to the solution of the original system under the large perturbation.

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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