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Pré-Publication, Document De Travail Année : 2015

A probabilistic approach to large time behaviour of viscosity solutions of parabolic equations with Neumann boundary conditions

Ying Hu
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Pierre-Yves Madec
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  • IdRef : 188413081

Résumé

This paper is devoted to the study of the large time behaviour of viscosity solutions of parabolic equations with Neumann boundary conditions. This work is the sequel of [13] in which a probabilistic method was developped to show that the solution of a parabolic semilinear PDE behaves like a linear term $\lambda T$ shifted with a function $v$, where $(v,\lambda)$ is the solution of the ergodic PDE associated to the parabolic PDE. We adapt this method in finite dimension by a penalization method in order to be able to apply an important basic coupling estimate result and with the help of a regularization procedure in order to avoid the lack of regularity of the coefficients in finite dimension. The advantage of our method is that it gives an explicit rate of convergence.
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Dates et versions

hal-01135840 , version 1 (26-03-2015)
hal-01135840 , version 2 (01-05-2015)
hal-01135840 , version 3 (17-09-2015)

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Ying Hu, Pierre-Yves Madec. A probabilistic approach to large time behaviour of viscosity solutions of parabolic equations with Neumann boundary conditions. 2015. ⟨hal-01135840v2⟩
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