CIORANESCU, D., MURAT, F. Un terme etrange venu d'ailleurs. Nonlinear partial differential equations and their applications, College de France seminar, Volume II, ed. by H.Brezis and J.L.Lions, Research Notes in Mathematics, Pitman, London (1982), 98-138. Home/Search Document Not in Database Summary Related Articles Check |
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A Rigorous Derivation of a Free-Boundary Problem Arising in.. - Sandier, Serfaty (1999) (Correct)
....of energy in the vortices, whereas 1 2 kh Gamma pk 2 H 1 corresponds to the remaining energy outside of [ i B i . This appears clearly in the proofs (see Section I.4 for a sketch) This phenomenon is of the same type as the one that was described by D. Cioranescu and F. Murat in [CM]. In this intermediate case h ex s Cjlog j (or 0 1) the energy that concentrates in the vortices (tending to the first term in E(h ) is of the same order as the energy outside of the vortex cores (which corresponds to the second term in E(h ) whereas when h ex AE jlog j, the outside ....
....to that of the upper bound of [SS2] in that it starts from the idea of constructing first a magnetic field satisfying Gamma Delta(h Gamma p) h = 2 P i ffi a i , where the a i s denote the vortices. Again, this construction, and particularly that of [SS2] has some similarity with that of [CM]. In [CM] they constructed a periodic function on a domain with small holes, corresponding to our vortex cores) whose number diverges. The scale of the holes relatively to their distances were the same as in our construction. Yet, one of the main differences here is that the test function is no ....
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D. Cioranescu and F. Murat, Un terme 'etrange venu d'ailleurs, Nonlinear partial differential equations and their applications, Coll. de France Semin., Vol. II, Res. Notes Math. 60, (1982), 98-138.
Homogenization Of Biharmonic Equations In Domains Perforated With.. - Huang (Correct)
....is oe = N N Gamma4 for N 4; and oe = exp Gamma 1 4 for N = 4: For the analogous problems of the second order equations with periodically distributed holes, the case when the size of the holes is much smaller than the period has been studied extensively in literatures. In [6], 11] and [8] the authors considered the problem for the Laplace equation. The homogenization for the wave equation in that case was studied in [5] The problem for the Navier Stokes equation was analyzed in [1] 2] These papers showed that the critical order for the second order equations is ....
.... Navier Stokes equation was analyzed in [1] 2] These papers showed that the critical order for the second order equations is oe = N N Gamma2 for N 2; and oe = exp Gamma 1 2 for N = 2: For homogenization of other equations and general references, we refer to [1] 2] 3] [6], 7] 10] 11] The proof of our results is based on the energy method. The main idea follows those in [1] 6] and [8] Since the different natures between the fourth order equations and the second order equations, the treatment here technically is different from the papers mentioned above. In ....
[Article contains additional citation context not shown here]
D. Cioranescu and F. Murat, Un terme 'etrange venu d'ailleurs, Nonlinear Partial Differential Equations and their Applications, Coll`ege de France Seminar: Vol. 2, 98-138, vol. 3, 154178, Pittman, London, 1982.
Propagation of Electromagnetic Waves in Non- Homogeneous Media - Alexandre, Taha (2002) (Correct)
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CIORANESCU, D., MURAT, F. Un terme etrange venu d'ailleurs. Nonlinear partial differential equations and their applications, College de France seminar, Volume II, ed. by H.Brezis and J.L.Lions, Research Notes in Mathematics, Pitman, London (1982), 98-138.
Scattering and Homogenization With Small Dipoles - Taha (2002) (Correct)
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CIORANESCU, D., MURAT, F. Un terme etrange venu d'ailleurs. Nonlinear partial differential equations and their applications, College de France seminar, Volume II, ed. by H.Brezis and J.L.Lions, Research Notes in Mathematics, Pitman, London (1982), 98-138.
Pinning phenomena in the Ginzburg-Landau Model of.. - Aftalion, Sandier (2000) (Correct)
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D. Cioranescu and F. Murat, Un terme 'etrange venu d'ailleurs, Nonlinear partial differential equations and their applications, Coll. de France Semin., Vol. II, Res. Notes Math. 60, (1982), 98-138.
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