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Opposing flows in a one dimensional convection-diffusion problem

Eugene O’Riordan (2012)

Open Mathematics

In this paper, we examine a particular class of singularly perturbed convection-diffusion problems with a discontinuous coefficient of the convective term. The presence of a discontinuous convective coefficient generates a solution which mimics flow moving in opposing directions either side of some flow source. A particular transmission condition is imposed to ensure that the differential operator is stable. A piecewise-uniform Shishkin mesh is combined with a monotone finite difference operator...

Optimal Convective Heat-Transport

Josef Dalík, Oto Přibyl (2011)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The one-dimensional steady-state convection-diffusion problem for the unknown temperature y ( x ) of a medium entering the interval ( a , b ) with the temperature y min and flowing with a positive velocity v ( x ) is studied. The medium is being heated with an intensity corresponding to y max - y ( x ) for a constant y max > y min . We are looking for a velocity v ( x ) with a given average such that the outflow temperature y ( b ) is maximal and discuss the influence of the boundary condition at the point b on the “maximizing” function v ( x ) .

Optimal design of turbines with an attached mass

Boris P. Belinskiy, C. Maeve McCarthy, Terry J. Walters (2003)

ESAIM: Control, Optimisation and Calculus of Variations

We minimize, with respect to shape, the moment of inertia of a turbine having the given lowest eigenfrequency of the torsional oscillations. The necessary conditions of optimality in conjunction with certain physical parameters admit a unique optimal design.

Optimal design of turbines with an attached mass

Boris P. Belinskiy, C. Maeve McCarthy, Terry J. Walters (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We minimize, with respect to shape, the moment of inertia of a turbine having the given lowest eigenfrequency of the torsional oscillations. The necessary conditions of optimality in conjunction with certain physical parameters admit a unique optimal design.

Oscillation and nonoscillation of higher order self-adjoint differential equations

Ondřej Došlý, Jan Osička (2002)

Czechoslovak Mathematical Journal

Oscillation and nonoscillation criteria for the higher order self-adjoint differential equation ( - 1 ) n ( t α y ( n ) ) ( n ) + q ( t ) y = 0 ( * ) are established. In these criteria, equation ( * ) is viewed as a perturbation of the conditionally oscillatory equation ( - 1 ) n ( t α y ( n ) ) ( n ) - μ n , α t 2 n - α y = 0 , where μ n , α is the critical constant in conditional oscillation. Some open problems in the theory of conditionally oscillatory, even order, self-adjoint equations are also discussed.

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