Application of homogenization and large deviations to a parabolic semilinear equation |
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Authors: | Alassane Diédhiou Clément Manga |
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Institution: | Département de Mathématiques, Informatique Faculté des Sciences et Technique, Université Cheikh Anta Diop, BP 5005, Dakar-Fann, Senegal |
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Abstract: | We study the behavior of the solution of a partial differential equation with a linear parabolic operator with non-constant coefficients varying over length scale δ and nonlinear reaction term of scale 1/?. The behavior is required as ? tends to 0 with δ small compared to ?. We use the theory of backward stochastic differential equations corresponding to the parabolic equation. Since δ decreases faster than ?, we may apply the large deviations principle with homogenized coefficients. |
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Keywords: | Homogenization Large deviations principle Viscosity solution Stochastic differential equation Backward stochastic differential equation |
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