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Article Dans Une Revue Stochastics and Dynamics Année : 2021

Penalization for a PDE with a Nonlinear Neumann boundary condition and measurable coefficients *

Résumé

We consider a system of semi-linear partial differential equations with measurable coefficients and a nonlinear Neumann boundary condition. We then construct a sequence of penalized partial differential equations which converges to a solution of our initial problem. The solution we construct is in the L p −viscosity sense, since the coefficients can be not continuous. The method we use is based on backward stochastic differential equations and their S-tightness. The present work is motivated by the fact that many partial differential equations arising in physics have discontinuous coefficients.
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Dates et versions

hal-02507957 , version 1 (13-03-2020)

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Khaled Bahlali, Brahim Boufoussi, Soufiane Mouchtabih. Penalization for a PDE with a Nonlinear Neumann boundary condition and measurable coefficients *. Stochastics and Dynamics, 2021, ⟨10.1142/S0219493721500532⟩. ⟨hal-02507957⟩
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