Limit of the Solution of a PDE in the Degenerate Case

DOI: 10.4236/am.2013.42051   PDF   HTML     2,942 Downloads   4,585 Views   Citations


In this paper we show that we can have the same conclusion for the limit of the solution if we suppose the case of hypoellipticity.

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A. Diedhiou, "Limit of the Solution of a PDE in the Degenerate Case," Applied Mathematics, Vol. 4 No. 2, 2013, pp. 338-342. doi: 10.4236/am.2013.42051.

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The authors declare no conflicts of interest.


[1] D. Nualart, “The Malliavin Calculus and Related Topics. Probability and Its Applications,” Springer-Verlag, New York, 1995.
[2] A. Diedhiou and C. Manga, “Application of Homogeneization and Large Deviations to a Parabolic Semilinear Equation,” Journal of Mathematical Analysis and Applications, Vol. 342, No. 1, 2008, pp. 146-160.
[3] M. I. Freidlin and R. B. Sowers, “A Comparison of Homogenization and Large Deviations, with Applications to Wavefront Propagation,” Stochastic Processes and Their Applications, Vol. 82, No. 1, 1999, pp. 23-32. doi:10.1016/S0304-4149(99)00003-4
[4] E. Pardoux and S. Peng, “Backward Stochastic Differential Equations and Quasi-Linear Parabolic Differential Equations,” In: B. L. Rozovskii and R. B. Sowers, Eds., Stochastic Partial Differential Equations and Their Applications, Lecture Notes in Control and Information Sciences, Vol. 176, 1992, pp. 200-217. doi:10.1007/BFb0007334
[5] A. Diédhiou and é. Pardoux, “Homogenization of Periodic Semilinear Hypoelliptic PDES,” Annales de la faculte des sciences de Toulouse Mathematiques, Vol. 16, No. 2, 2007, pp. 253-283.
[6] E. Pardoux, “Homogenization of Linear and Semilinear Second Order Parabolic PDEs with Periodic Coefficients: A Probabilistic Approch,” Journal of Functional Analysis, Vol. 167, No. 2, 1999, pp. 498-520. doi:10.1006/jfan.1999.3441
[7] E. Pardoux, “BSDEs, Weak Convergence and Homogenization of Semilinear PDEs,” In: F. H. Clarke and R. J. Stern, Eds., Nonlinear Analysis, Differential Equations and Control, Springer, Berlin, 1999, pp. 503-549.
[8] A. Dembo and O. Zeitouni, “Large Deviations Techniques and Applications,” Jones and Bartlett, Boston, 2010.

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