Singular large diffusivity and spatial homogenization in a non homogeneous linear parabolic problem
| dc.contributor.author | Rodríguez Bernal, Aníbal | |
| dc.contributor.author | Willie, Robert | |
| dc.date.accessioned | 2023-06-20T09:45:13Z | |
| dc.date.available | 2023-06-20T09:45:13Z | |
| dc.date.issued | 2005-05 | |
| dc.description.abstract | We make precise the sense in which spatial homogenization to a constant function in space is attained in a linear parabolic problem when large diffusion in all parts of the domain is assumed. Also interaction between diffusion and boundary flux terms is considered. Our starting point is a detailed analysis of the large diffusion effects on the associated elliptic and eigenvalue problems. Here convergence is shown in the energy space H-1(Omega) and in the space of continuous functions C(Omega). In the parabolic case we prove convergence in the functional space L-infinity((0, T), L-2(Omega)) boolean AND L-2((0, T), H-1(Omega)). | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/17781 | |
| dc.identifier.doi | 10.3934/dcdsb.2005.5.385 | |
| dc.identifier.issn | 1531-3492 | |
| dc.identifier.officialurl | http://www.aimsciences.org/journals/displayArticles.jsp?paperID=939 | |
| dc.identifier.relatedurl | http://www.aimsciences.org/index.html | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/50303 | |
| dc.issue.number | 2 | |
| dc.journal.title | Discrete and Continuous Dynamical Systems. Series B. A Journal Bridging Mathematics and Sciences | |
| dc.language.iso | eng | |
| dc.page.final | 410 | |
| dc.page.initial | 385 | |
| dc.publisher | American Institute of Mathematical Sciences | |
| dc.relation.projectID | BFM2003-03810 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.986 | |
| dc.subject.keyword | Linear parabolic problem | |
| dc.subject.keyword | Non homogeneous boundary conditions | |
| dc.subject.keyword | Linear elliptic problem | |
| dc.subject.keyword | Eigenvalue problem | |
| dc.subject.keyword | Large diffusion | |
| dc.subject.keyword | Analytic semigroups | |
| dc.subject.keyword | Convergence of solutions | |
| dc.subject.keyword | Nonlinear boundary-conditions | |
| dc.subject.keyword | Attractors | |
| dc.subject.keyword | Equations | |
| dc.subject.keyword | Behavior | |
| dc.subject.keyword | Systems | |
| dc.subject.ucm | Funciones (Matemáticas) | |
| dc.subject.unesco | 1202 Análisis y Análisis Funcional | |
| dc.title | Singular large diffusivity and spatial homogenization in a non homogeneous linear parabolic problem | |
| dc.type | journal article | |
| dc.volume.number | 5 | |
| dcterms.references | H. Amann, Dual Semigroups and Second Order Linear Elliptic Boundary Value Problems, Israel Journal of Mathematics, 45 (1983), no. 2–3, 225–254. H. Amann & J. López-Gómez, A Priori Bounds and Multiple Solutions for Superlinear Indefinite Elliptic Problems, J. Differential Equations, 146 (1998), no. 2, 336–374. J. Arrieta, A.Carvalho and A.Rodríguez—Bernal, Attractors of Parabolic Problems with Non-linear Boundary Conditions. Uniform Bounds., Communications in Partial Differential Equations, 25 (2000), 1/2, 1–37. J.Arrieta, A.Carvalho and A.Rodríguez—Bernal, Upper Semicontinuity for Attractors of Parabolic Problems with Localized Large Diffusion and Nonlinear Boundary Conditions. Journal of Differential Equations, 168 (2000), 33–59. A. N. Carvalho, Infinite Dimensional Dynamics Described by Ordinary Differential Equations, Journal of Differential Equations, 116 (1995), no. 2, 338–404. A.N. Carvalho, J.K. Hale, Large diffusion with dispersion. Nonlinear Anal., 17 (1991), no. 12, 1139–1151. R. Courant and D. Hilbert, Methods of Mathematical Physics, Intersciences Publishers, New York 1953. 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), no. 1, 1–16. J. M. Fraile, P.K. Medina, J. López Gómez and S. Merino, Elliptic Eigenvalue Problems and Unbounded Continua of Positive Solutions of a Semilinear Elliptic Equation, J. Diff. Eqs., 127 (1996), no. 1, 295–319. D. Gilbarg and N.S.Trudinger, Elliptic Partial Differential Equations of Second Order, Grundlehren der mathematischen Wissenschaften 224, Springer-Verlag, 1983. J. K. Hale, Large Diffusivity and Asymptotic Behavior in Parabolic Systems, J. Math. Anal and Appl, 118 (1986), 455–466. J.K.Hale and C. Rocha, Varying Boundary Conditions with Large Diffusivity. J. Math. Pures et Appl., 66 (1987), 139–158. D. Henry, Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Mathematics, 840 (1981), Springer-Verlag. J. López Gómez, The Maximum Principle and the Existence of Principal Eigenvalues for Some Linear Wieghted Boundary Value Problems J. Diff. Eqs., 127 (1996), 263–294. O. Ladyzhenskaya and N Ural'tseva, Linear and quasilinear elliptic equations. Academic Press New York and London, 1968. O. A. Ladyzhenskaya, N.N Ural'tseva & V.A Solonnikov, Linear and quasilinear equations of parabolic type. Amer. Math. Soc. Providence R.I., Translations of Mathematical Monographs, 23 (1968). J. L. Lions & E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, Vol.I, Springer-Verlag, New York, 1972. A. Rodríguez-Bernal, Lecture Notes of the Course: Semilinear Evolution Equations. Universidad Complutense de Madrid, Spain. 1996. A. Rodríguez-Bernal, Localized spatial homogenization and large diffusion. Siam J. Math. Anal., 29 (1998), no. 6, 1361–1380. A. Rodríguez-Bernal and E. Zuazua, Parabolic singular limit of a wave equation with localized boundary damping, Journal of Discrete and Continuous Dynamical Systems, 1 (1995), no. 3, 303–346. R. Willie, Upper semi-continuity of Attractors for a semilinear reaction and diffusion system of Equation in sup norm, To appear. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | fb7ac82c-5148-4dd1-b893-d8f8612a1b08 | |
| relation.isAuthorOfPublication.latestForDiscovery | fb7ac82c-5148-4dd1-b893-d8f8612a1b08 |
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