Some results about the approximate controllability property for quasilinear diffusion equations
| dc.contributor.author | Díaz Díaz, Jesús Ildefonso | |
| dc.contributor.author | Ramos Del Olmo, Ángel Manuel | |
| dc.date.accessioned | 2023-06-20T16:54:44Z | |
| dc.date.available | 2023-06-20T16:54:44Z | |
| dc.date.issued | 1997-06 | |
| dc.description.abstract | We study the approximate controllability property for y(t) - Delta phi(y) = u chi(omega), on Omega x (0, T), where Omega is a bounded open set of R-N and omega subset of Omega. First, we show some negative results for the case phi(s) = \s\(m-1)s, 0 < m < 1, by means of an obstruction phenomenon. In a second part, we obtain a positive answer on the space H-1-gamma(Omega), for any gamma > 0, for a class of functions phi essentially linear at infinity, by using a higher order vanishing viscosity argument. | |
| 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/15821 | |
| dc.identifier.doi | 10.1016/S0764-4442(99)80407-8 | |
| dc.identifier.issn | 0764-4442 | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/S0764444299804078 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57404 | |
| dc.issue.number | 11 | |
| dc.journal.title | Comptes Rendus de l'Académie des Sciences. Série I. Mathématique | |
| dc.language.iso | fra | |
| dc.page.final | 1248 | |
| dc.page.initial | 1243 | |
| dc.publisher | Elsevier | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.977 | |
| dc.subject.keyword | quasilinear diffusion equation | |
| dc.subject.keyword | approximate controllability | |
| dc.subject.ucm | Ecuaciones diferenciales | |
| dc.subject.unesco | 1202.07 Ecuaciones en Diferencias | |
| dc.title | Some results about the approximate controllability property for quasilinear diffusion equations | |
| dc.type | journal article | |
| dc.volume.number | 324 | |
| dcterms.references | C. Bandle, M. Markus. “Large” solutions of semilinear elliptic equations: existence, uniqueness and asymptotic behaviour. Journal d'Analyse Mathématique, 58 (1992), pp. 9–24 H. Brézis. Monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations. E. Zarantonello (Ed.), Nonlinear Functional Analysis, Academic Press (1971), pp. 101–156 H. Brézis. Opérateurs Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert. North-Holland, New York (1973) A. Damlamian. Some results on the multi-phase Stefan problem. Comm. Part. Diff. Eq., 2 (1977), pp. 1017–1044 J.I. Díaz, A.M. Ramos. On the Approximate Controllability for Higher Order Parabolic Nonlinear Equations of Cahn-Hilliard Type. To appear in Proceedings of the International Conference on Control and Estimation of DistributedParameter Systems (1997). C. Fahre, J.P. Puel, E. Zuazua. Approximate controllability of the semilinear heat equation. Proceedings of the Royal Society of Edinburgh, 125A (1995), pp. 31–61 M.A. Herrero, M. Pierre. The Cauchy Problem for ut = Δum when 0 < m < 1. Trans. Amer. Math.Soc., 291 (1985), pp. 145–158 A.S. Kalashnikov. Some problems of the qualitative theory of nonlinear degenerate second-order parabolic equations. Russ. Math. Survs., 42 (1987), pp. 169–222 J.-L.Lions. Remarques sur la contrôlabilité approchée.Proceedings of Jornadas Hispano-Francesas sobreControl de Sistemas Distribuidos, Univ. de Malaga, Vorau (Austria) (1990), pp. 77–88 J. Simon. Compact Sets in the Space Lp(0, T;B). Serie 4 Annali di Mat. Pura ed Appl., 146 (1987), pp. 65–96. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 34ef57af-1f9d-4cf3-85a8-6a4171b23557 | |
| relation.isAuthorOfPublication | 581c3cdf-f1ce-41e0-ac1e-c32b110407b1 | |
| relation.isAuthorOfPublication.latestForDiscovery | 34ef57af-1f9d-4cf3-85a8-6a4171b23557 |
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