HOMOGENIZATION OF A DEGENERATE PDE WITH
NON LINEAR WENTZELL BOUNDARY CONDITION

Abstract

We develop homogenization results of a degenerate semilinear PDE with a Wentzell-type boundary condition. The second order operator is also degenerate. Our approach is entirely probabilistic, and extends the result of Diakhaby and Ouknine [3].

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 30
Issue: 1
Year: 2017

DOI: 10.12732/ijam.v30i1.3

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References

  1. [1] A. Jakubowski, A non-Skorohod topology on the Skorohod space, Electronic J. of Prob., 2 (1997), 1-21.
  2. [2] E. Pardoux and A. Diedhiou, Homogenization of periodic semilinear hypoelliptic PDES, Anal. Fac. Scien. de Toulouse Math., 16 (2007), 253-283.
  3. [3] A. Diakhby and Y. Ouknine, Generalized BSDEs, weak convergence, and homogenization of semilinear PDEs with the Wentzell-type boundary condition, Stoch. Analysis and Appl., 3 (2016), 493-509.
  4. [4] E. Pardoux and Yu.A. Veretennikov, On the Poisson equation and diffusion approximation I, Annals of Probability, 29 (2001), 1061-1085.
  5. [5] E. Pardoux and S. Zhang, Generalized BSDEs and nonlinear boundary value problems, Prob. Theory and Rel. Fields, 110 (1998), 535-558.
  6. [6] H. Tanaka, Homogenization of diffusion processes with boundary conditions, Stoc. Anal. and Appl., Adv. Probab. Related Topics, 7 (1984), 411-437.