Noetherity of a Dirac Delta-Extension for a Noether Operator
Abdourahman,
Ecclésiaste Tompé Weimbapou,
Emmanuel Kengne
Issue:
Volume 8, Issue 3, June 2022
Pages:
51-57
Received:
27 April 2022
Accepted:
17 May 2022
Published:
26 May 2022
DOI:
10.11648/j.ijtam.20220803.11
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Abstract: The main goal of this work is to establish the extension of a noether operator defined by a third kind singular integral equation in a special class of generalized functions and to investigate the noetherity of the extended operator. The initial considered operator has been investigated for its noetherity nature in our previous works. Special approach has been developed and applied when constructing noether theory for the mentioned operator by using the concept of Taylor derivatives for continuous functions to achieve noetherity. We realize the extension of the initial noether operator defined onto the class of coninuous functions, having first continous derivative and taking the value zero at the left boundary point of the closed interval by adding a finite number of Dirac delta functions and it Taylor derivatives of some order. Then, we investigate the noetherity of the extended initial noether operator when we realize the finite dimensional extension, taking the unknown function from a special space of generalized functions. For this aim, we will use the direct formal calculations and apply the principle of the conservation of the index of noether operator after it finite dimensional extension in the new constructed functional space. The noetherity of the extended operator is established and the deficient numbers with the corresponding index are calculated in various cases investigated.
Abstract: The main goal of this work is to establish the extension of a noether operator defined by a third kind singular integral equation in a special class of generalized functions and to investigate the noetherity of the extended operator. The initial considered operator has been investigated for its noetherity nature in our previous works. Special appro...
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Upshot of Slip Velocity and Thermal Radiation on Magnetohydrodynamic Transient Fluid Flow Through Vertical Walls
Bashiru Abdullahi,
Isah Bala Yabo,
Ibrahim Yakubu Seini,
Murtala Muhammed Hamza
Issue:
Volume 8, Issue 3, June 2022
Pages:
65-77
Received:
16 February 2022
Accepted:
7 March 2022
Published:
29 September 2022
DOI:
10.11648/j.ijtam.20220803.13
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Abstract: Transient MHD heat transfer within radiative channel due to convective boundary and slip velocity is considered. Non-linear Roseland approximation was used to describe the radiative heat flux in the energy equation where the magnetic field is combined in the momentum equation. The solution of the governing differential equation that described the flow was solved using the Perturbation method in order to obtain the analytical solution which was used to confirm the validity of the numerical solution. The finite difference method was employed to find the numerical solution of the governing equations. The heat transfer device of the present work establishes the influence of Biot number, slip parameter (λ), magnetizing parameter, radiation parameter, temperature difference, Grashof number and time on velocity, temperature, skin friction, and Nusselt number. The results established were discoursed with the aid of line graphs. The steady-state solution was in perfect agreement with the transient form for the weighty value of time t. It is exciting to report that the convective boundary condition and slip velocity has a strong impact on the flow parameters.
Abstract: Transient MHD heat transfer within radiative channel due to convective boundary and slip velocity is considered. Non-linear Roseland approximation was used to describe the radiative heat flux in the energy equation where the magnetic field is combined in the momentum equation. The solution of the governing differential equation that described the f...
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-neighbourhood while the concerned difference inequality is in an