On the homogenization of weakly nonlinear divergent operators in a perforated cube. (English. Russian original) Zbl 1018.35032
Math. Notes 68, No. 3, 337-344 (2000); translation from Mat. Zametki 68, No. 3, 390-398 (2000).
Summary: In the present paper we consider a second-order weakly nonlinear elliptic equation of divergent form with a lower term growing at infinity (with respect to the unknown function) as a power function. It is proved that a sequence of solutions in the perforated cubes converges to a solution in the nonperforated cube as the diameters of the holes tends to zero, and the rate of convergence depends on the power exponent of the lower term.
MSC:
| 35J60 | Nonlinear elliptic equations |
| 35B27 | Homogenization in context of PDEs; PDEs in media with periodic structure |
| 47F05 | General theory of partial differential operators |
Keywords:
equation with sufficiently strong nonlinear absorbtions; sequence of solutions; rate of convergenceReferences:
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