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Applicable Analysis
An International Journal
Volume 86, 2007 - Issue 7
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Original Articles

Asymptotics for eigenelements of Laplacian in domain with oscillating boundary: multiple eigenvalues

Youcef Amirat Laboratoire de Mathématiques, CNRS UMR 6620, Université Blaise Pascal, 63177 Aubière cedex, France
,
Gregory A. Chechkin Faculty of Mechanics and Mathematics, Department of Differential Equations, Moscow Lomonosov State University, Moscow 119992, Russia; Narvik University College, Postboks 385, 8505 Narvik, NorwayCorrespondence[email protected]
&
Rustem R. Gadyl'shin Faculty of Physics and Mathematics, Department of Mathematical Analysis, Bashkir State Pedagogical University, Ufa 450000, Russia
Pages 873-897 | Received 06 Feb 2007, Accepted 16 May 2007, Published online: 27 Sep 2007

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Youcef Amirat & Olivier Bodart. (2010) Stokes equations with interface condition in an unbounded domain. Applicable Analysis 89:1, pages 29-47.
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Siwar Saidani & Abdessatar Khelifi. Eigenoscillations of the Maxwell equation in a domain with oscillating boundary. Complex Variables and Elliptic Equations 0:0, pages 1-16.
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Articles from other publishers (23)

Ahlem Jaouabi & Abdessatar Khelifi. (2023) Asymptotic behavior for eigenvalues and eigenfunctions associated to Stokes operator in the presence of a rapidly oscillating boundary. Mathematical Methods in the Applied Sciences 47:4, pages 1915-1939.
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Saoussen Boujemaa & Abdessatar Khelifi. (2023) Asymptotic expansion for solution of Maxwell equation in domain with highly oscillating boundary. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 103:10.
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Ahlem Jaouabi & Abdessatar Khelifi. (2023) Asymptotic property for eigenelements of the Laplace operator in a domain with an oscillating boundary. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 103:8.
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Shun-Liang Zhang & Zhi-Hui Wang. (2023) Theoretical modelling of non-equilibrium reaction–diffusion of rarefied gas on a wall with microscale roughness. Journal of Fluid Mechanics 965.
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Abdessatar Khelifi & Ahlem Jaouabi. (2022) On the asymptotic formulas for perturbations in the eigenvalues of the Stokes equations due to the presence of small deformable inclusions. Journal of Applied Analysis 28:1, pages 149-164.
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R. R. Gadyl'shin, A. L. Piatnitskii & G. A. Chechkin. (2018) On the asymptotic behaviour of eigenvalues of a boundary-value problem in a planar domain of Steklov sieve type. Izvestiya: Mathematics 82:6, pages 1108-1135.
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Rustem Rashitovich Gadyl'shin, Andrey Lvovich Piatnitski & Gregory Aleksandrovich Chechkin. (2018) Об асимптотиках собственных значений краевой задачи в плоской области типа сита СтекловаOn the asymptotic behaviour of eigenvalues of a boundary-value problem in a planar domain of Steklov sieve type. Известия Российской академии наук. Серия математическая Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya 82:6, pages 37-64.
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R. I. Bihun & Z. V. Stasyuk. (2016) Impact of Surface Inhomogeneities on Conditions for Charge Transfer in Ultrathin Films of Metals. METALLOFIZIKA I NOVEISHIE TEKHNOLOGII 36:6, pages 723-734.
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R.I. Bihun, Z.V. Stasyuk & O.A. Balitskii. (2016) Crossover from quantum to classical electron transport in ultrathin metal films. Physica B: Condensed Matter 487, pages 73-77.
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D.-H. Nguyen, H.-T. Le, H. Le Quang & Q.-C. He. (2014) Determination of the effective conductive properties of composites with curved oscillating interfaces by a two-scale homogenization procedure. Computational Materials Science 94, pages 150-162.
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V. M. Hut. (2014) Asymptotic Expansions of Eigenvalues and Eigenfunctions of a Vibrating System With Stiff Light-Weight Inclusions. Journal of Mathematical Sciences 198:1, pages 13-30.
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Denis Borisov, Giuseppe Cardone, Luisa Faella & Carmen Perugia. (2013) Uniform resolvent convergence for strip with fast oscillating boundary. Journal of Differential Equations 255:12, pages 4378-4402.
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T. P. Chechkina. (2013) Averaging in Cascade Junctions with a “Wide” Transmission Domain. Journal of Mathematical Sciences 190:1, pages 157-169.
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H. Le Quang, Q.-C. He & H.-T. Le. (2013) Multiscale Homogenization of Elastic Layered Composites with Unidirectionally Periodic Rough Interfaces. Multiscale Modeling & Simulation 11:4, pages 1127-1148.
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Youcef Amirat, Olivier Bodart, Gregory A. Chechkin & Andrey L. Piatnitski. (2011) Boundary homogenization in domains with randomly oscillating boundary. Stochastic Processes and their Applications 121:1, pages 1-23.
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Youcef Amirat, Gregory A. Chechkin & Rustem R. Gadyl’shin. (2010) Spectral boundary homogenization in domains with oscillating boundaries. Nonlinear Analysis: Real World Applications 11:6, pages 4492-4499.
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G. A. Chechkin, C. D'Apice & U. De Maio. (2010) On the rate of convergence of solutions in domain with periodic multilevel oscillating boundary. Mathematical Methods in the Applied Sciences 33:17, pages 2019-2036.
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Youcef Amirat, Gregory A. Chechkin & Rustem R. Gadyl'shin. (2010) Asymptotic approximation of eigenelements of the Dirichlet problem for the Laplacian in a domain with shoots. Mathematical Methods in the Applied Sciences 33:7, pages 811-830.
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Pham Chi Vinh & Do Xuan Tung. (2010) Homogenized equations of the linear elasticity in two-dimensional domains with very rough interfaces. Mechanics Research Communications 37:3, pages 285-288.
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T. A. Mel’nik, G. A. Chechkin & T. P. Chechkina. (2009) Convergence theorems for solutions and energy functionals of boundary value problems in thick multilevel junctions of a new type with perturbed neumann conditions on the boundary of thin rectangles. Journal of Mathematical Sciences 159:1, pages 113-132.
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Тарас Анатольевич Мельник, Taras Anatol'evich Mel'nik, Григорий Александрович Чечкин, Gregory Aleksandrovich Chechkin, Григорий Александрович Чечкин & Gregory Aleksandrovich Chechkin. (2009) Асимптотический анализ краевых задач в густых трехмерных многоуровневых соединенияхAsymptotic analysis of boundary-value problems in thick three-dimensional multi-level junctions. Математический сборник Matematicheskii Sbornik 200:3, pages 49-74.
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T. A. Mel’nik & G. A. Chechkin. (2008) Homogenization of a boundary value problem in a thick cascade junction. Journal of Mathematical Sciences 154:1, pages 50-77.
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Youcef Amirat, Gregory A. Chechkin & Rustem R. Gadyl'shin. (2008) Asymptotics of the solution of a Dirichlet spectral problem in a junction with highly oscillating boundary. Comptes Rendus. Mécanique 336:9, pages 693-698.
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