Homogenization of periodic elliptic degenerate PDEs with non-linear Neumann boundary condition
In this paper, a semi-linear elliptic partial differential equation (PDE) with non linear Neumann boundary condition and rapidly oscillating coefficients is homogenized. The novelty of our result lies in the fact that we allow the second order part of the differential operator to be degenerate in so...
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2021-06-01
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doaj-d7dd264d528142609daa35eed8469b502021-06-05T06:10:58ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812021-06-013100021Homogenization of periodic elliptic degenerate PDEs with non-linear Neumann boundary conditionMohamed Marzougue0Ibrahima Sane1Laboratory LAMA, Faculty of Sciences Agadir, Ibn Zohr University, Agadir, Morocco; Corresponding author.UFR ST, Assane SECK University of Ziguinchor, Ziguinchor, SenegalIn this paper, a semi-linear elliptic partial differential equation (PDE) with non linear Neumann boundary condition and rapidly oscillating coefficients is homogenized. The novelty of our result lies in the fact that we allow the second order part of the differential operator to be degenerate in some portion of Rd. Our fully probabilistic method is based on the connection between PDEs and backward stochastic differential equations (BSDEs) with random terminal time and the weak convergence of a class of diffusion processes.http://www.sciencedirect.com/science/article/pii/S2666818121000012HomogenizationElliptic degenerate PDEsNeumann-boundary conditionStochastic differential equationBackward stochastic differential equation |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Mohamed Marzougue Ibrahima Sane |
spellingShingle |
Mohamed Marzougue Ibrahima Sane Homogenization of periodic elliptic degenerate PDEs with non-linear Neumann boundary condition Partial Differential Equations in Applied Mathematics Homogenization Elliptic degenerate PDEs Neumann-boundary condition Stochastic differential equation Backward stochastic differential equation |
author_facet |
Mohamed Marzougue Ibrahima Sane |
author_sort |
Mohamed Marzougue |
title |
Homogenization of periodic elliptic degenerate PDEs with non-linear Neumann boundary condition |
title_short |
Homogenization of periodic elliptic degenerate PDEs with non-linear Neumann boundary condition |
title_full |
Homogenization of periodic elliptic degenerate PDEs with non-linear Neumann boundary condition |
title_fullStr |
Homogenization of periodic elliptic degenerate PDEs with non-linear Neumann boundary condition |
title_full_unstemmed |
Homogenization of periodic elliptic degenerate PDEs with non-linear Neumann boundary condition |
title_sort |
homogenization of periodic elliptic degenerate pdes with non-linear neumann boundary condition |
publisher |
Elsevier |
series |
Partial Differential Equations in Applied Mathematics |
issn |
2666-8181 |
publishDate |
2021-06-01 |
description |
In this paper, a semi-linear elliptic partial differential equation (PDE) with non linear Neumann boundary condition and rapidly oscillating coefficients is homogenized. The novelty of our result lies in the fact that we allow the second order part of the differential operator to be degenerate in some portion of Rd. Our fully probabilistic method is based on the connection between PDEs and backward stochastic differential equations (BSDEs) with random terminal time and the weak convergence of a class of diffusion processes. |
topic |
Homogenization Elliptic degenerate PDEs Neumann-boundary condition Stochastic differential equation Backward stochastic differential equation |
url |
http://www.sciencedirect.com/science/article/pii/S2666818121000012 |
work_keys_str_mv |
AT mohamedmarzougue homogenizationofperiodicellipticdegeneratepdeswithnonlinearneumannboundarycondition AT ibrahimasane homogenizationofperiodicellipticdegeneratepdeswithnonlinearneumannboundarycondition |
_version_ |
1721396528646455296 |