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Relevant bibliographies by topics / Oscillating boundary domains

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Journal articles

Academic literature on the topic 'Oscillating boundary domains'

Author: Grafiati

Published: 6 September 2023

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Journal articles on the topic "Oscillating boundary domains"

1

Amirat, Youcef, Olivier Bodart, Gregory A. Chechkin, and Andrey L. Piatnitski. "Boundary homogenization in domains with randomly oscillating boundary." Stochastic Processes and their Applications 121, no. 1 (2011): 1–23. http://dx.doi.org/10.1016/j.spa.2010.08.011.

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2

Amirat, Youcef, Gregory A. Chechkin, and Rustem R. Gadyl’shin. "Spectral boundary homogenization in domains with oscillating boundaries." Nonlinear Analysis: Real World Applications 11, no. 6 (2010): 4492–99. http://dx.doi.org/10.1016/j.nonrwa.2008.11.023.

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3

Chechkin, Gregory A., Avner Friedman, and Andrey L. Piatnitski. "The Boundary-value Problem in Domains with Very Rapidly Oscillating Boundary." Journal of Mathematical Analysis and Applications 231, no. 1 (1999): 213–34. http://dx.doi.org/10.1006/jmaa.1998.6226.

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4

Aiyappan, S., A. K. Nandakumaran, and Ravi Prakash. "Semi-linear optimal control problem on a smooth oscillating domain." Communications in Contemporary Mathematics 22, no. 04 (2019): 1950029. http://dx.doi.org/10.1142/s0219199719500299.

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We demonstrate the asymptotic analysis of a semi-linear optimal control problem posed on a smooth oscillating boundary domain in the present paper. We have considered a more general oscillating domain than the usual “pillar-type” domains. Consideration of such general domains will be useful in more realistic applications like circular domain with rugose boundary. We study the asymptotic behavior of the problem under consideration using a new generalized periodic unfolding operator. Further, we are studying the homogenization of a non-linear optimal control problem and such non-linear problems

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5

Eger, V., O. A. Oleinik, and T. A. Shaposhnikova. "Homogenization of boundary value problems in domains with rapidly oscillating nonperiodic boundary." Differential Equations 36, no. 6 (2000): 833–46. http://dx.doi.org/10.1007/bf02754407.

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6

Feldman, William M. "Homogenization of the oscillating Dirichlet boundary condition in general domains." Journal de Mathématiques Pures et Appliquées 101, no. 5 (2014): 599–622. http://dx.doi.org/10.1016/j.matpur.2013.07.003.

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7

OULD-HAMMOUDA, AMAR, and RACHAD ZAKI. "Homogenization of a class of elliptic problems with nonlinear boundary conditions in domains with small holes." Carpathian Journal of Mathematics 31, no. 1 (2015): 77–88. http://dx.doi.org/10.37193/cjm.2015.01.09.

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We consider a class of second order elliptic problems in a domain of RN , N > 2, ε-periodically perforated by holes of size r(ε) , with r(ε)/ε → 0 as ε → 0. A nonlinear Robin-type condition is prescribed on the boundary of some holes while on the boundary of the others as well as on the external boundary of the domain, a Dirichlet condition is imposed. We are interested in the asymptotic behavior of the solutions as ε → 0. We use the periodic unfolding method introduced in [Cioranescu, D., Damlamian, A. and Griso, G., Periodic unfolding and homogenization, C. R. Acad. Sci. Paris, Ser. I, 33

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8

Pettersson, Irina. "Two-scale convergence in thin domains with locally periodic rapidly oscillating boundary." Differential Equations & Applications, no. 3 (2017): 393–412. http://dx.doi.org/10.7153/dea-2017-09-28.

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9

Zhuge, Jinping. "First-order expansions for eigenvalues and eigenfunctions in periodic homogenization." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 5 (2019): 2189–215. http://dx.doi.org/10.1017/prm.2019.8.

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AbstractFor a family of elliptic operators with periodically oscillating coefficients, $-{\rm div}(A(\cdot /\varepsilon )\nabla )$ with tiny ε > 0, we comprehensively study the first-order expansions of eigenvalues and eigenfunctions (eigenspaces) for both the Dirichlet and Neumann problems in bounded, smooth and strictly convex domains (or more general domains of finite type). A new first-order correction term is introduced to derive the expansion of eigenfunctions in L2 or $H^1_{\rm loc}$. Our results rely on the recent progress on the homogenization of boundary layer problems.

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10

Piatnitski, A., and V. Rybalko. "Homogenization of boundary value problems for monotone operators in perforated domains with rapidly oscillating boundary conditions of fourier type." Journal of Mathematical Sciences 177, no. 1 (2011): 109–40. http://dx.doi.org/10.1007/s10958-011-0450-3.

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