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Upper semicontinuity for attractors of parabolic problems with localized large diffusion and nonlinear boundary conditions

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Arrieta Algarra, José María and Carvalho, Alexandre N. and Rodríguez Bernal, Aníbal (2000) Upper semicontinuity for attractors of parabolic problems with localized large diffusion and nonlinear boundary conditions. Journal of Differential Equations, 168 (1). pp. 33-59. ISSN 0022-0396

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Official URL: http://www.sciencedirect.com/science/article/pii/S0022039600938762




Abstract

The motivations to study the problem considered in this paper come from the theory of composite materials, where the heat diffusion properties can change from one part of the domain to another. Mathematically, this leads to a nonlinear second-order parabolic equation for which the diffusion coefficient becomes large in a subdomain Ω 0 ⊂Ω . The equation is supplemented by a nonlinear boundary condition on ∂Ω and an initial condition. The authors determine the form of the limit problem (the so-called shadow system), which involves an evolution equation for the averages of the density over Ω 0 . The main results include global-in-time existence of solutions and upper semicontinuity of the associated global attractors when the system approaches the shadow system.


Item Type:Article
Uncontrolled Keywords:Second-order parabolic problems; Diffusion coefficient becomes large in a Subregion of the domain; Asymptotic-behavior; Equations; Systems
Subjects:Sciences > Mathematics > Functions
ID Code:19979
Deposited On:15 Feb 2013 17:27
Last Modified:12 Dec 2018 15:07

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