periodical problem
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2017 ◽  
Vol 27 (7) ◽  
pp. 1451-1466 ◽  
Author(s):  
Tomáš Neustupa

Purpose The paper aims to theoretically study the mathematical model of a steady flow of a heat-conductive incompressible viscous fluid through a spatially periodic plane profile cascade. Design/methodology/approach Reduction of the infinite periodical problem to one period. Leray-Schauder fixed point principle was used. Findings This study proves the existence of a weak solution for arbitrarily large given data (i.e. the inflow velocity and the acting specific body force). Practical implications The author proposed a special boundary condition on the outflow of the domain not only for the velocity and pressure but also for the temperature. Originality/value To the author’s knowledge, the problem has not been studied earlier. More detailed overview is given in the paper in the first part.



1991 ◽  
Vol 14 (3) ◽  
pp. 581-586
Author(s):  
M. G. El Sheikh ◽  
A. H. Khater ◽  
D. K. Callebaut

The stationary periodical problem of a vibrating rectangular plate, stressed at a segment while fixed elsewhere at one of its edges, is considered. Using the finite Fourier transformation, the problem is converted to a singular integral equation that in turn can be reduced to an infinite system of algebraic equations. The truncation of the algebraic system is justified.



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