Locally periodic homogenization. (English) Zbl 1064.35017

Benchérif-Madani, A.; Pardoux, É.

Asymptotic Anal. 39, No. 3-4, 263-279 (2004).

Summary: Two linear second-order (an elliptic bvp and parabolic ivp) PDEs are homogenized. The coefficients are supposed to be locally periodic, Lipschitz and bounded. Compared to a previous work of the authors [Lect. Notes Math. 1857, 363–392 (2005; Zbl 1067.35009)], they provide a new and simpler proof and weaken the hypotheses of the main theorem. Both probabilistic and analytic arguments are used.

MSC:

35B27	Homogenization in context of PDEs; PDEs in media with periodic structure
35J25	Boundary value problems for second-order elliptic equations
35K15	Initial value problems for second-order parabolic equations

Keywords:

diffusion approximation; probabilistic and analytic arguments

Citations:

Zbl 1067.35009