Stable boundary layers in a diffusion problem with nonlinear reaction at the boundary
| dc.contributor.author | Arrieta Algarra, José María | |
| dc.contributor.author | Cónsul, Neus | |
| dc.contributor.author | Rodríguez Bernal, Aníbal | |
| dc.date.accessioned | 2023-06-20T09:46:30Z | |
| dc.date.available | 2023-06-20T09:46:30Z | |
| dc.date.issued | 2004 | |
| dc.description.abstract | We prove the existence of nonconstant stable stationary solutions of an evolution problem with a nonlinear reaction acting on the boundary. These solutions present layers at certain points of the boundary. We also study the behavior of these solutions as the small parameter appearing in the equation approaches zero and show some stability properties of the profiles given by these equilibrium solutions. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | CICYT | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/18119 | |
| dc.identifier.doi | 10.1007/s00033-003-2063-z | |
| dc.identifier.issn | 0044-2275 | |
| dc.identifier.officialurl | http://download.springer.com/static/pdf/453/art%253A10.1007%252Fs00033-003-2063-z.pdf?auth66=1360940295_9a26f43517b93d290ff05a6bb450d133&ext=.pdf | |
| dc.identifier.relatedurl | http://link.springer.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/50338 | |
| dc.issue.number | 1 | |
| dc.journal.title | Zeitschrift für Angewandte Mathematik und Physik | |
| dc.language.iso | eng | |
| dc.page.final | 14 | |
| dc.page.initial | 1 | |
| dc.publisher | Springer Verlag | |
| dc.relation.projectID | BFM2000-0798 | |
| dc.relation.projectID | PB98-0932-C02-01 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.9 | |
| dc.subject.keyword | Boundary reaction | |
| dc.subject.keyword | Patterns | |
| dc.subject.keyword | Boundary layers | |
| dc.subject.keyword | Energy | |
| dc.subject.keyword | Minimizers | |
| dc.subject.keyword | Heat-equations | |
| dc.subject.keyword | Spaces | |
| dc.subject.keyword | Bounds | |
| dc.subject.keyword | Time | |
| dc.subject.keyword | Nonconstant equilibria | |
| dc.subject.keyword | Parabolic problems | |
| dc.subject.keyword | Transition layers | |
| dc.subject.keyword | Equations | |
| dc.subject.keyword | Attractors | |
| dc.subject.keyword | Stability | |
| dc.subject.ucm | Ecuaciones diferenciales | |
| dc.subject.unesco | 1202.07 Ecuaciones en Diferencias | |
| dc.title | Stable boundary layers in a diffusion problem with nonlinear reaction at the boundary | |
| dc.type | journal article | |
| dc.volume.number | 55 | |
| dcterms.references | S. Angenent, J. Mallet-Paret, L. Peletier, Stable transition layers in a semilinear boundary Value Problem, Journal of Differential Equations 67 (1987), 212-242. J.M. Arrieta, A.N. Carvalho and A. Rodríguez-Bernal, Parabolic problems with nonlinear boundary conditions and critical nonlinearities. Journal of Differential Equations 156 (1999), 376-406. J.M. Arrieta, A.N. Carvalho and A. Rodríguez-Bernal, Attractors of parabolic problems with nonlinear boundary conditions. Uniform bounds, Comm. in Partial Diff. Equations 25 (2000), 1-37. J.M. Arrieta, N. Cónsul, A. Rodríguez-Bernal, Pattern formation from boundary reaction, Fields Inst. Comm.31 (2002), 13-18. N. Cónsul, On equilibrium solutions of diffusion equations with nonlinear boundary conditions, Z. Angew. Math. Phys. 47 (1996), 194-209. N. Cónsul, J. Solà-Morales, Stable nonconstant equilibria in parabolic equations with nonlinear boundary conditions, C.R. Acad. Sci. Paris, T. 321, Sèrie I, (1995), 299-304. N. Cónsul, J. Solà-Morales, Stability of local minima and stable nonconstant equilibria, Journal of Differential Equations 157 (1999), 61-81. A. do Nascimento, Inner transition layers in a elliptic boundary value problem”, Nonl. Anal.: Th. Meth. and Appl. 44 (2001), 487–497. R. Casten, C. Holland, Stability properties of solutions to systems of reaction-diffusion equations, SIAM J. Appl. Math. 33 (1977), 353–364. H. Matano, Asymptotic behavior and stability of solutions of semilinear diffusion equations, Publ. Res. Inst. Math. Sci. 15 (1979), 401-451. C. Rocha, Examples of attractors in scalar reaction diffusion equations, Journal of Differential Equations 73 (1988), 178-195. Equations 73 (1988), 178-195. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 2f8ee04e-dfcb-4000-a2ae-18047c5f0f4a | |
| relation.isAuthorOfPublication | fb7ac82c-5148-4dd1-b893-d8f8612a1b08 | |
| relation.isAuthorOfPublication.latestForDiscovery | 2f8ee04e-dfcb-4000-a2ae-18047c5f0f4a |
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