Arrieta Algarra, José María and Pereira, Marcone C. (2011) Homogenization in a thin domain with an oscillatory boundary. Journal de Mathématiques Pures et Appliquées, 96 (1). pp. 2957. ISSN 00217824

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Abstract
In this paper we analyze the behavior of the Laplace operator with Neumann boundary conditions in a thin domain of the type where the function G(x,y) is periodic in y of period L. Observe that the upper boundary of the thin domain presents a highly oscillatory behavior and, moreover, the height of the thin domain, the amplitude and period of the oscillations are all of the same order, given by the small parameter ϵ.
Item Type:  Article 

Uncontrolled Keywords:  Thin domain; Oscillating boundary; Homogenization; Extension operator 
Subjects:  Sciences > Mathematics > Differential equations 
ID Code:  13402 
References:  [1] Y. Amirat, O. Bodart, U. de Maio, A. Gaudiello, “Asymptotic Approximation of the solution of the Laplace equation in a domain with highly oscillating boundary", SIAM J. Math. Anal. 35, 15981616 (2004) [2] J. M. Arrieta, Spectral properties of Schrödinger operators under perturbations of the domain, Ph.D. Thesis, Georgia Institute of Technology, (1991) [3] J. M. Arrieta and M. C. Pereira, “Elliptic problems in thin domains with highly oscillating boundaries", Bol. Soc. Esp. Mat. Apl., to appear. [4] J. M. Arrieta, A. N. Carvalho, M. C. Pereira and R. P. da Silva; “Attractors in thin domains with a highly oscillatory boundary", Submitted. [5] A. Bensoussan, J. L. Lions and G. Papanicolaou, Asymptotic Analysis for Periodic Structures, NorthHolland Publishing Company (1978). [6] R. Brizzi, J.P. Chalot, “Boundary homogenization and Neumann boundary problem" Ricerce di Matematica XLVI, 2 (1997) 341387 [7] V. Burenkov, P.D. Lamberti, “Spectral Stability of general nonnegarive selfadjoint operators with applications to Neumanntype operators", J. Differential Equations 233 (2007), 345379 [8] D. Cioranescu and J. Saint Jean Paulin; Homogenization of Reticulated Structures, Springer Verlag (1980). [9] A. Damlamian, K. Pettersson, “Homogenization of oscillating boundaries" , Discrete and Continuous Dynamical Systems 23, (2009), 197219 [10] J. K. Hale and G. Raugel, “Reactiondiffusion equation on thin domains", J. Math. Pures and Appl. (9) 71, no. 1, 3395 (1992). [11] G. Raugel; Dynamics of partial differential equations on thin domains in Dynamical systems (Montecatini Terme, 1994), 208315, Lecture Notes in Math., 1609, Springer, Berlin, 1995. [12] E. SánchezPalencia, NonHomogeneous Media and Vibration Theory, Lecture Notes in Physics 127, Springer Verlag (1980) [13] L. Tartar; Problèmmes d'homogénéisation dans les équations aux dérivées partielles, Cours Peccot, Collège de France (1977). [14] L. Tartar, “Quelques remarques sur l'homegénéisation", Function Analysis and Numerical Analysis, Proc. JapanFrance Seminar 1976, ed. H. Fujita, Japanese Society for the Promotion of Science, 468482 (1978). 
Deposited On:  14 Oct 2011 07:24 
Last Modified:  06 Feb 2014 09:48 
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