Localized spatial homogenization and large diffusion

dc.contributor.authorRodríguez Bernal, Aníbal
dc.date.accessioned2023-06-20T17:10:29Z
dc.date.available2023-06-20T17:10:29Z
dc.date.issued1998-11
dc.description.abstractWe analyze singular perturbations in elliptic equations, subjected to various boundary conditions, in which the diffusion is going to infinity in localized regions inside the domain and therefore solutions undergo a localized spatial homogenization. The limiting elliptic operator is analyzed as well as convergence of solutions, eigenvalues, and eigenvectors.
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/19836
dc.identifier.doi10.1137/S003614109731864X
dc.identifier.issn0036-1410
dc.identifier.officialurlhttp://epubs.siam.org/doi/pdf/10.1137/S003614109731864X
dc.identifier.relatedurlhttp://epubs.siam.org/
dc.identifier.urihttps://hdl.handle.net/20.500.14352/57890
dc.issue.number6
dc.journal.titleSIAM Journal on Mathematical Analysis
dc.page.final1380
dc.page.initial1361
dc.publisherSociety for Industrial and Applied Mathematics
dc.rights.accessRightsmetadata only access
dc.subject.cdu517.9
dc.subject.keywordSingular perturbation
dc.subject.keywordEigenvalue problems
dc.subject.keywordLarge diffusion
dc.subject.keywordConvergence
dc.subject.keywordLinear elliptic boundary value problems
dc.subject.keywordLimiting elliptic problem
dc.subject.keywordDifferential-equations
dc.subject.keywordAsymptotic-behavior
dc.subject.keywordConstruction
dc.subject.keywordSystems
dc.subject.ucmEcuaciones diferenciales
dc.subject.unesco1202.07 Ecuaciones en Diferencias
dc.titleLocalized spatial homogenization and large diffusion
dc.typejournal article
dc.volume.number29
dcterms.referencesS. S. Antman, Nonlinear Problems of Elasticity, Springer-Verlag, New York, 1995. H. Brezis and T. Kato, Remarks on the Schr"odinger operator with complex potentials, J. Math. Pures Appl., 58 (1979), pp. 137–151. A. N. Carvalho, Spatial homogeneity in damped hyperbolic equations, Dynam. Systems Appl., 1 (1992), pp. 221–250. A. N. Carvalho and J. K. Hale, Large diffusion with dispersion, Nonlinear Anal., 17 (1991), pp. 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), pp. 81–130. A. N. Carvalho and L. A. F. Oliveira, Delay–partial differential equations with some large diffusion, Nonlinear Anal., 22 (1994), pp. 1057–1095. A. N. Carvalho and A. Rodriguez-Bernal, Upper Semicontinuity of Attractors for Parabolic Equations with Localized Large Diffusion and Nonlinear Boundary Conditions, in preparation. P. G. Ciarlet, Mathematical Elasticity, North–Holland, Amsterdam, 1988. E. Conway, D. Hoff, and J. Smoller, Large time behavior of solutions of systems of non- linear reaction-diffusion equations, SIAM J. Appl. Math., 35 (1978), pp. 1–16. G. Fusco, On the explicit construction of an ODE which has the same dynamics as a scalar parabolic PDE, J. Differential Equations, 69 (1987), pp. 85–110. J. Hale, Large diffusivity and asymptotic behavior in parabolic systems, J. Math. Anal. Appl., 118 (1986), pp. 455–466. J. Hale and C. Rocha, Varying boundary conditions and large diffusivity, J. Math. Pures Appl., 66 (1987), pp. 139–158. J. K. Hale and K. Sakamoto, Shadow systems and attractors in reaction-diffusion equations, Appl. Anal., 32 (1989), pp. 287–303. T. Kato, Perturbation Theory of Linear Operators, Springer-Verlag, New York, 1980. A. Rodriguez-Bernal, On the construction of inertial manifolds under symmetry constraints II: O(2) constraint and inertial manifolds on thin domains, J. Math. Pures Appl., 72 (1993), pp. 57–79. J. Sánchez-Hubert and E. Sánchez-Palencia, Vibration and Coupling of Continuous Sys- tems. Asymptotic Methods, Springer-Verlag, New York, 1989. G. Stampacchia, Le probléme de Dirichlet por les 'equations elliptiques du second ordre `a coefficients discontinus, Ann. Inst. Fourier-Grenoble, 15 (1965), pp. 189–258. M. Valencia and J. Solá-Morales, Trend to spatial homogeneity for solutions of semilinear damped wave equations, Proc. Roy. Soc. Edinburgh Sect. A, 105 (1987), pp. 117–126.
dspace.entity.typePublication
relation.isAuthorOfPublicationfb7ac82c-5148-4dd1-b893-d8f8612a1b08
relation.isAuthorOfPublication.latestForDiscoveryfb7ac82c-5148-4dd1-b893-d8f8612a1b08

Download

Collections