Well-Posed Problems for a Partial Differential Equation of Order $2m + 1$

1970 ◽  
Vol 1 (2) ◽  
pp. 214-231 ◽  
Author(s):  
R. E. Showalter
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Partial Differential ◽  
Well Posed

THE STOCHASTIC MAGNETO-HYDRODYNAMIC SYSTEM

1999 ◽  
Vol 02 (02) ◽  
pp. 241-265 ◽  
Author(s):  
S. S. SRITHARAN ◽  
P. SUNDAR
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
White Noise ◽  
Stochastic Partial Differential Equation ◽  
Martingale Problem ◽  
Partial Differential ◽  
Hydrodynamic System ◽  
Well Posed

The magneto-hydrodynamic system perturbed by white noise is cast as a stochastic partial differential equation taking values in an appropriate Lusin space. The martingale problem associated with this SPDE is shown to be well-posed under suitable conditions.

Tikhonov Regularization Solve Partial Differential Equations Inverse Problem

2011 ◽  
Vol 50-51 ◽  
pp. 459-462
Author(s):  
Ya Li He ◽  
Shi Qiu Zheng ◽  
Yan Mei Yang
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Inverse Problem ◽  
Approximate Solution ◽  
Partial Differential Equations ◽  
General Theory ◽  
Tikhonov Regularization ◽  
Related Concept ◽  
Partial Differential ◽  
Well Posed

This article discussed the partial differential equation inverse problem. Because the partial differential equation inverse is the misalignment improperly posed problem, therefore analyzed has had the improperly posed reason. To process the partial differential equation inverse correctly not well-posed ness this difficulty, obtains relies on continuously the data stable approximate solution, has drawn support from the regularization related concept and the regularization general theory.

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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