Nesting inertial manifolds for reaction and diffusion equations with large diffusivity
| dc.contributor.author | Rodríguez Bernal, Aníbal | |
| dc.contributor.author | Willie, Robert | |
| dc.date.accessioned | 2023-06-20T09:44:33Z | |
| dc.date.available | 2023-06-20T09:44:33Z | |
| dc.date.issued | 2007-07-01 | |
| dc.description.abstract | We study the asymptotic behaviour in large diffusivity of inertial manifolds governing the long time dynamics of a semilinear evolution system of reaction and diffusion equations. A priori, we review both local and global dynamics of the system in scales of Banach spaces of Hilbert type and we prove the existence of a universal compact attractor for the equations. Extensions yield the existence of a family of nesting inertial manifolds dependent on the diffusion of the system of equations. It is introduced an upper semicontinuity notion in large diffusivity for inertial manifolds. The limit inertial manifold whose dimension is strictly less than those of the infinite dimensional system of semilinear evolution equations is obtained. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | Ministry of Higher Education (Spain) | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/17693 | |
| dc.identifier.doi | 10.1016/j.na.2006.05.017 | |
| dc.identifier.issn | 0362-546X | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/S0362546X06003233 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/50283 | |
| dc.issue.number | 1 | |
| dc.journal.title | Nonlinear Analysis: Theory, Methods & Applications | |
| dc.language.iso | eng | |
| dc.page.final | 93 | |
| dc.page.initial | 70 | |
| dc.publisher | Elsevier | |
| dc.relation.projectID | BFM 2003-03810 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.986 | |
| dc.subject.keyword | Semilinear system of reaction-diffusion equations | |
| dc.subject.keyword | Well posedness | |
| dc.subject.keyword | Universal compact attractor | |
| dc.subject.keyword | Inertial manifolds | |
| dc.subject.keyword | Limit inertial manifold | |
| dc.subject.keyword | Large diffusivity | |
| dc.subject.ucm | Funciones (Matemáticas) | |
| dc.subject.unesco | 1202 Análisis y Análisis Funcional | |
| dc.title | Nesting inertial manifolds for reaction and diffusion equations with large diffusivity | |
| dc.type | journal article | |
| dc.volume.number | 67 | |
| dcterms.references | R. Adams, Sobolev Spaces, Academic Press, New York, 1975. H. Amann, Linear and quasilinear parabolic problems, Vol. I, in: Abstract Linear Theory, Birkhäuser, 1995. H. Amann, Parabolic evolution equations and nonlinear boundary conditions, Journal of Differential Equations 72 (1988) 201–269. J. Arrieta, A. Rodríguez-Bernal, A.N. de Carvalho, Critical nonlinear at boundary, C. R. Acad. Sci. Paris t. 327, Serie I (1998) 353–358. H. Brézis, Análisis Functional Teoría y Applicaciones, Editorial Alianza Universidad Textos, Masson, Paris, 1983. A.N. Caravalho, Infinite dimensional dynamics described by ordinary differential equations, Journal of Differential Equations 116 (1995) 338–404. A.N. Caravalho, J.W. Cholewa, T. Dlotko, Examples of global attractors in parabolic problems, Hokkaido Mathematical Journal 27 (1998) 77–103. R. Courant, D. Hilbert, Methods of Mathematical Physics, Interscience Publishers, New York, 1953. E. Conway, D. Hoff, J. Smoller, Large time behaviour of solutions of systems of nonlinear reaction and diffusion equations, SIAM Journal on Applied Mathematics 35 (1) (1978) 1–16. S.N. Chow, K. Lu, Invariant manifold for flows in Banach spaces, Journal of Differential Equations 74 (1988) 285–317. C. Foias, G.R. Sell, R. Temam, Inertial manifold for nonlinear evolutionary equations, Journal of Differential Equations 73 (1988) 309–353. J.K. Hale, Large diffusivity and asymptotic behaviour in parabolic systems, Journal of Mathematical Analysis and Applications 118 (1986) 455–466. J.K. Hale, Asymptotic Behaviour of Dissipative Systems, in: Mathematical Surveys and Monographs, vol. 25, AMS, 1988. J.K. Hale, C. Rocha, Varying boundary conditions with large diffusivity, Nonlinear Analysis, Theory, Methods and Applications 11 (5) (1987) 633–649. D. Henry, Geometric Theory of Semilinear Parabolic Equations, in: Lecture Notes in Mathematics, vol. 840, Springer-Verlag, 1981. A. Lunardi, Analytic Semigroups and Optimal Regularity in Parabolic Problems, in: Progress in Nonlinear Differential Equations and their Applications, vol. 16, Birkhäuser, 1995. M. Renardy, R.C. Rogers, An Introduction to Partial Differential Equations, in: T.A.M., vol. 13, Springer-Verlag, 1992. A. Rodríguez Bernal, Ecuaciones de evolución semilineales, in: Lecture Notes, Universidad Complutense de Madrid, 1996–1997. A. Rodríguez Bernal, Existence, uniqueness and regularity of solutions of evolution equations in extended scales of Hilbert spaces, in: CDSNS Gatech report series, 1991. A. Rodríguez Bernal, Inertial manifold for dissipative semiflows in Banach spaces, Applicable Analysis 37 (1990) 95–141. R. Temam, Infinite Dimensional Dynamical Systems in Mechanics and Physics, second ed., in: Applied Mathematical Sciences, vol. 68, Springer-Verlag, 1997. G.R. Sell, Y. You, Inertial manifold: The non self adjoint case, Journal of Differential Equations 96 (1992) 203–255. G.R. Sell, Y. You, Dynamics of Evolutionary Equations, in: Applied Mathematical Sciences, vol. 143, Springer-Verlag, 2002. R. Willie, Reaction and diffusion equations with large diffusivity, D.Sc. Maths. Thesis. University of Madrid, Complutense, 2005. R. Willie, A semilinear reaction–diffusion system of equations and large diffusion, Journal of Dynamics and Differential Equations 16 (1) (2004) 35–63. R. Willie, Structural large diffusivity stability of attractors in C(Ω ) topology for a semilinear reaction–diffusion system of equations, Dynamics of Partial Differential Equations (in press). R. Willie, Singular large diffusivity and spatial homogenization in a non homogeneous linear parabolic problem. Discrete and Continuous Dynamical Systems. Series B 5 (2) (2005) 385–410. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | fb7ac82c-5148-4dd1-b893-d8f8612a1b08 | |
| relation.isAuthorOfPublication.latestForDiscovery | fb7ac82c-5148-4dd1-b893-d8f8612a1b08 |
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