Upper semicontinuity for attractors of parabolic problems with localized large diffusion and nonlinear boundary conditions
| dc.contributor.author | Arrieta Algarra, José María | |
| dc.contributor.author | Carvalho, Alexandre N. | |
| dc.contributor.author | Rodríguez Bernal, Aníbal | |
| dc.date.accessioned | 2023-06-20T17:11:28Z | |
| dc.date.available | 2023-06-20T17:11:28Z | |
| dc.date.issued | 2000-11-20 | |
| dc.description.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. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | DGICYT (Spain) | |
| dc.description.sponsorship | CNPq (Brazil) | |
| dc.description.sponsorship | FAPESP (Brazil) | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/19979 | |
| dc.identifier.doi | 10.1006/jdeq.2000.3876 | |
| dc.identifier.issn | 0022-0396 | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/S0022039600938762 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com/science | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57917 | |
| dc.issue.number | 1 | |
| dc.journal.title | Journal of Differential Equations | |
| dc.language.iso | eng | |
| dc.page.final | 59 | |
| dc.page.initial | 33 | |
| dc.publisher | Elsevier | |
| dc.relation.projectID | PB96-0648 | |
| dc.relation.projectID | 300.889/92-5 | |
| dc.relation.projectID | #97/11323-0 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.986 | |
| dc.subject.keyword | Second-order parabolic problems | |
| dc.subject.keyword | Diffusion coefficient becomes large in a Subregion of the domain | |
| dc.subject.keyword | Asymptotic-behavior | |
| dc.subject.keyword | Equations | |
| dc.subject.keyword | Systems | |
| dc.subject.ucm | Funciones (Matemáticas) | |
| dc.subject.unesco | 1202 Análisis y Análisis Funcional | |
| dc.title | Upper semicontinuity for attractors of parabolic problems with localized large diffusion and nonlinear boundary conditions | |
| dc.type | journal article | |
| dc.volume.number | 168 | |
| dcterms.references | H. Amann, Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems, in "Schmeisser/Triebel: Function Spaces, Differential Operators and Nonlinear Analysis," Teubner Texte zur Mathematik, Vol. 133, pp. 9–126, Teubner, Leipzig, 1993. J. M. Arrieta and A. N. Carvalho, Abstract parabolic problems with critical nonlinearities and applications to Navier-Stokes and heat equations, Trans. Amer. Math. Soc. 352 (2000), 285–310. J. M. Arrieta, A. N. Carvalho, and A. Rodriguez-Bernal, Parabolic problems with nonlinear boundary conditions and critical nonlinearities, J. Differential Equations 156 (1999), 376–406. J. M. Arrieta, A. N. Carvalho, and A. Rodriguez-Bernal, Attractors of parabolic problems whith nonlinear boundary conditions: Uniform bounds, Comm. Partial Differential Equations 25 (2000), 1–37. A. N. Carvalho and J. K. Hale, Large diffusion with dispersion, Nonlinear Anal. 17 (1991), 1139–1151. A. N. Carvalho and A. L. Pereira, A scalar parabolic equation whose asymptotic behavior is dictated by a system of ordinary differential equations, J. Differential Equations 112 (1994), 81–130. E. Conway, D. Hoff, and J. Smoller, Large time behavior of solutions of systems of nonlinear reaction-diffusion equations, SIAM J. Appl. Math. 35 (1978), 1–16. J. Hale, Large diffusivity and asymptotic behavior in parabolic systems, J. Math. Anal. Appl. 118 (1986), 455–466. J. K. Hale, "Asymptotic Behavior of Dissipative Systems," Mathematical Surveys and Monographs, Vol. 25, Amer. Math. Soc., Providence, RI, 1988. J. K. Hale and G. Raugel, Upper semicontinuity of the attractor for a singularly perturbed hyperbolic equation, J. Differential Equations 73 (1988), 197–214. J. Hale and C. Rocha, Varying boundary conditions and large diffusivity, J. Math Pures Appl. 66 (1987), 139–158. J. K. Hale and K. Sakamoto, Shadow systems and attractors in reaction-diffusion equations, Appl. Anal. 32 (1989), 287–303. D. Henry, "Geometric Theory of Semilinear Parabolic Equations," Lecture Notes in Mathematics, Vol. 840, Springer-Verlag, Berlin, 1981. O. Ladyzenskaya and N. Uraltseva, "Linear and Quasilinear Elliptic Equations," Academic Press, New York, 1968. MR0244627 A. Pazy, "Semigroups of Linear Operators and Applications to Partial Differential Equations," Applied Math. Sci., Vol. 44, Springer-Verlag, New York, 1983. A. Rodriguez-Bernal, Localized spatial homogenization and large diffusion, SIAM J. Math. Anal. 29 (1998), 1361–1380. | |
| dspace.entity.type | Publication | |
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| relation.isAuthorOfPublication.latestForDiscovery | 2f8ee04e-dfcb-4000-a2ae-18047c5f0f4a |
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