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Akademický článek

On shape and topological optimization problems with constraints Helmholtz equation and spectral problems

Autor: Mame Gor Ngom, Ibrahima Faye, Diaraf Seck

Publikováno v: Results in Applied Mathematics, Vol 23, Iss , Pp 100474- (2024)

Coastal erosion describes the displacement of sand caused by the movement induced by tides, waves or currents. Some of its wave phenomena are modelled by Helmholtz-type equations. Our purposes, in this paper are, first, to study optimal shapes obstac

Externí odkaz: https://doaj.org/article/c4c12d7d8368401085863f951b9adadd

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Akademický článek

Shape derivative for obstacles in crowd motion

Autor: Boubacar Fall, Filippo Santambrogio, Diaraf Seck

Publikováno v: Mathematics in Engineering, Vol 4, Iss 2, Pp 1-16 (2022)

We consider different PDE modeling for crowd motion scenarios, or other sort of fluid flows, and we insert in the given domain R an obstacle O. We then compute the shape derivatives of a cost functional, the average exit time, in order to be able to

Externí odkaz: https://doaj.org/article/70df19465ca34d39bb2dc5eaa03a3708

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Akademický článek

Existence of solutions for the one-phase and the multi-layer free-boundary problems with the p-laplacian operator

Autor: Idrissa Ly, Diaraf Seck

Publikováno v: Electronic Journal of Differential Equations, Vol 2006, Iss 128, Pp 1-23 (2006)

By considering the p-laplacian operator, we show the existence of a solution to the exterior (resp interior) free boundary problem with non constant Bernoulli free boundary condition. In the second part of this article, we study the existence of solu

Externí odkaz: https://doaj.org/article/215ad0ba3b4e4030b742e91be27237c1

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Akademický článek

Isoperimetric inequality for an interior free boundary problem with p-laplacian operator

Autor: drissa Ly, Diaraf Seck

Publikováno v: Electronic Journal of Differential Equations, Vol 2004, Iss 109, Pp 1-12 (2004)

By considering the p-Laplacian operator, we establish an existence and regularity result for a shape optimization problem. From a monotony result, we show the existence of a solution to the interior problem with a free surface for a family of Bernoul

Externí odkaz: https://doaj.org/article/32952fbc343c415582b99af9878ab848

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Akademický článek

Topological Optimization with the p-Laplacian Operator and an Application in Image Processing

Autor: Alassane Sy, Diaraf Seck

Publikováno v: Boundary Value Problems, Vol 2009 (2009)

We focus in this paper on the theoretical and numerical aspect os image processing. We consider a non linear boundary value problem (the p-Laplacian) from which we will derive the asymptotic expansion of the Mumford-Shah functional. We give a theoret

Externí odkaz: https://doaj.org/article/10be54217f9c4954a775bba96270e72b

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