Positivity for large time of solutions of the heat equation: The parabolic antimaximum principle
| dc.contributor.author | Díaz Díaz, Jesús Ildefonso | |
| dc.contributor.author | Fleckinger-Pellé, Jacqueline | |
| dc.date.accessioned | 2023-06-20T09:35:20Z | |
| dc.date.available | 2023-06-20T09:35:20Z | |
| dc.date.issued | 2004 | |
| dc.description.abstract | We study the positivity, for large time, of the solutions to the heat equation Q(a) (f,u(0)): [GRAPHIC] where Q is a smooth bounded domain in RN and a C R. We obtain some sufficient conditions for having a finite time t(p) > 0 (depending on a and on the data u(0) and f which are not necessarily of the same sign) such that u(t, x) > 0 For Allt > t(p), a.e.x is an element of Omega. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | DGES (Spain) | |
| dc.description.sponsorship | EC | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/15471 | |
| dc.identifier.issn | 1078-0947 | |
| dc.identifier.officialurl | http://aimsciences.org/journals/pdfs.jsp?paperID=139&mode=full | |
| dc.identifier.relatedurl | http://aimsciences.org/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/49976 | |
| dc.issue.number | 1-2 | |
| dc.journal.title | Discrete and Continuous Dynamical Systems. Series A. | |
| dc.language.iso | eng | |
| dc.page.final | 200 | |
| dc.page.initial | 193 | |
| dc.publisher | American Institute of Mathematical Sciences | |
| dc.relation.projectID | REN2000-0766 | |
| dc.relation.projectID | RTN HPRN-CT- | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.95 | |
| dc.subject.keyword | maximum and antimaximum principle | |
| dc.subject.keyword | heat equation | |
| dc.subject.keyword | parabolic problems | |
| dc.subject.ucm | Geometría diferencial | |
| dc.subject.ucm | Ecuaciones diferenciales | |
| dc.subject.unesco | 1204.04 Geometría Diferencial | |
| dc.subject.unesco | 1202.07 Ecuaciones en Diferencias | |
| dc.title | Positivity for large time of solutions of the heat equation: The parabolic antimaximum principle | |
| dc.type | journal article | |
| dc.volume.number | 10 | |
| dcterms.references | Amann, H., Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Review, 18, N. 4, 620–709, (1976). Antontsev, S.N., Diaz, J.I., Shmarev, S.I. Energy Methods for free bounday problems. Applications to nonlinear PDEs and Fluid Mechanics, Series Progress in Nonlinear Differential Equations and Their Applications, No. 48, Birkäuser, Boston, (2002). Bertsch, M., Peletier, L.A., The asymptotic profile of solutions of a degenerate diffusion equation, Arch. Rat. Mech. Anal. 91, 207–229, (1985). Ph. Clément, L. A. Peletier, An anti-maximum principle for second order elliptic operators, J. Differential Equations 34, 218–229, (1979). Díaz, J.I., Morel, J.M., Sur les solutions de l'équation de la chaleur, unpublished manuscript, (1986). Díaz, J.I., de Thélin, F., On a nonlinear parabolic problem arising in some models related to turbulent flows, SIAM J. Math. Anal., 25, 4, 1085–1111, (1994). Fleckinger, J., Gossez, J.P., Takáč, P., de Thélin, F., Non existence of solutions and an antimaximum principle for cooperative systems with the p - Laplacian, Math. Nachrichten, 194, 49–78, (1998). Gmira, A., Véron, L., Asymptotic Behaviour of the Solution of a Semilinear Parabolic Equation, Monatsh.Math. 94, 299–311, (1982). Sattinger, D., Monotone methods in nonlinear elliptic and parabolic boundary value problems, Indiana Univ. Math J., 21, 979–1000, (1972). | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 34ef57af-1f9d-4cf3-85a8-6a4171b23557 | |
| relation.isAuthorOfPublication.latestForDiscovery | 34ef57af-1f9d-4cf3-85a8-6a4171b23557 |
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