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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 an elastic beam with a unilateral elastic foundation: semicoercive state problem

Roman Šimeček (2013)

Applications of Mathematics

A design optimization problem for an elastic beam with a unilateral elastic foundation is analyzed. Euler-Bernoulli's model for the beam and Winkler's model for the foundation are considered. The state problem is represented by a nonlinear semicoercive problem of 4th order with mixed boundary conditions. The thickness of the beam and the stiffness of the foundation are optimized with respect to a cost functional. We establish solvability conditions for the state problem and study the existence of...

Raman laser : mathematical and numerical analysis of a model

François Castella, Philippe Chartier, Erwan Faou, Dominique Bayart, Florence Leplingard, Catherine Martinelli (2004)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper we study a discrete Raman laser amplification model given as a Lotka-Volterra system. We show that in an ideal situation, the equations can be written as a Poisson system with boundary conditions using a global change of coordinates. We address the questions of existence and uniqueness of a solution. We deduce numerical schemes for the approximation of the solution that have good stability.

Raman laser: mathematical and numerical analysis of a model

François Castella, Philippe Chartier, Erwan Faou, Dominique Bayart, Florence Leplingard, Catherine Martinelli (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we study a discrete Raman laser amplification model given as a Lotka-Volterra system. We show that in an ideal situation, the equations can be written as a Poisson system with boundary conditions using a global change of coordinates. We address the questions of existence and uniqueness of a solution. We deduce numerical schemes for the approximation of the solution that have good stability.

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