Homogenization of boundary value problems for monotone operators in\n perforated domains with rapidly oscillating boundary conditions of Fourier\n type

2010/06/03 by Andrey Piatnitski, Piatnitski, Andrey, Volodymyr Rybalko +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #Differential Equations and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.1006.0615

openalex publication_date 2010/06/03 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

The paper deals with homogenization problem for nonlinear elliptic and\nparabolic equations in a periodically perforated domain, a nonlinear Fourier\nboundary conditions being imposed on the perforation border. Under the\nassumptions that the studied differential equation satisfies monotonicity and\n2-growth conditions and that the coefficient of the boundary operator is\ncentered at each level set of unknown function, we show that the problem under\nconsideration admits homogenization and derive the effective model.\n

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