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Asymptotic behaviour of solutions of boundary-value problems for equations with rapidly oscillating coefficients in a domain with a small cavity. / Nazarov, S. A.; Slutskiǐ, A.
в: Sbornik Mathematics, Том 189, № 9-10, 01.01.1998, стр. 1385-1422.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Asymptotic behaviour of solutions of boundary-value problems for equations with rapidly oscillating coefficients in a domain with a small cavity
AU - Nazarov, S. A.
AU - Slutskiǐ, A.
PY - 1998/1/1
Y1 - 1998/1/1
N2 - Asymptotic representations of the solutions of boundary-value problems for a second-order equation with rapidly oscillating coefficients in a domain with a small cavity (of diameter comparable with the period of oscillation) are found and substantiated. Dirichlet or Neumann conditions are set at the boundary of the domain. In addition to an asymptotic series of structure standard for homogenization theory there occur terms describing the boundary layer phenomenon near the opening, while the solutions of the homogenized problem and their rapidly oscillating correctors acquire singularities at the contraction point of the openings. The dimension of the domain and some other factors influence even the leading term of the asymptotic formula. Some generalizations, including ones to the system of elasticity theory, are discussed.
AB - Asymptotic representations of the solutions of boundary-value problems for a second-order equation with rapidly oscillating coefficients in a domain with a small cavity (of diameter comparable with the period of oscillation) are found and substantiated. Dirichlet or Neumann conditions are set at the boundary of the domain. In addition to an asymptotic series of structure standard for homogenization theory there occur terms describing the boundary layer phenomenon near the opening, while the solutions of the homogenized problem and their rapidly oscillating correctors acquire singularities at the contraction point of the openings. The dimension of the domain and some other factors influence even the leading term of the asymptotic formula. Some generalizations, including ones to the system of elasticity theory, are discussed.
UR - http://www.scopus.com/inward/record.url?scp=0038911671&partnerID=8YFLogxK
U2 - 10.1070/SM1998v189n09ABEH000353
DO - 10.1070/SM1998v189n09ABEH000353
M3 - Article
AN - SCOPUS:0038911671
VL - 189
SP - 1385
EP - 1422
JO - Sbornik Mathematics
JF - Sbornik Mathematics
SN - 1064-5616
IS - 9-10
ER -
ID: 40992154