On the melting of ice balls
| dc.contributor.author | Herrero, Miguel A. | |
| dc.contributor.author | Velázquez, J.J. L. | |
| dc.date.accessioned | 2023-06-20T17:08:45Z | |
| dc.date.available | 2023-06-20T17:08:45Z | |
| dc.date.issued | 1997-01 | |
| dc.description | Existe una errata en el artículo. Las fórmulas (1.2) y (1.4) deben ser reemplazadas por las (1.12) y (1.13) de la versión posterior del artículo ("A note on the dissolution of spherical analysis") disponible en http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=1201356&fulltextType=RA&fileId=S0308210500000913 | |
| dc.description.abstract | We consider here the problem of describing the melting of an ice ball surrounded by water. The corresponding mathematical model consists of the Stefan problem with radial symmetry. We obtain asymptotic expansions for the radius of the melting ball which turn out to be of a different nature according to the cases N greater than or equal to 3 and N = 2, N being the space dimension. The methods employed combine matched asymptotic expansion techniques, a priori estimates, and topological results. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.faculty | Instituto de Matemática Interdisciplinar (IMI) | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/17922 | |
| dc.identifier.doi | 10.1137/S0036141095282152 | |
| dc.identifier.issn | 0036-1410 | |
| dc.identifier.officialurl | http://epubs.siam.org/simax/resource/1/sjmaah/v28/i1/p1_s1?isAuthorized=no | |
| dc.identifier.relatedurl | http://epubs.siam.org | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/57840 | |
| dc.issue.number | 1 | |
| dc.journal.title | Siam Journal on Mathematical Analysis | |
| dc.language.iso | eng | |
| dc.page.final | 32 | |
| dc.page.initial | 1 | |
| dc.publisher | Society for Industrial and Applied Mathematics | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.956.4 | |
| dc.subject.cdu | 536.2 | |
| dc.subject.keyword | Stefan problem | |
| dc.subject.keyword | asymptotic behavior | |
| dc.subject.keyword | matched asymptotic expansions | |
| dc.subject.keyword | a priori estimates | |
| dc.subject.keyword | semilinear heat-equations | |
| dc.subject.keyword | blow-up | |
| dc.subject.keyword | parabolic equations | |
| dc.subject.ucm | Ecuaciones diferenciales | |
| dc.subject.unesco | 1202.07 Ecuaciones en Diferencias | |
| dc.title | On the melting of ice balls | |
| dc.type | journal article | |
| dc.volume.number | 28 | |
| dcterms.references | D. G. ARONSON AND S. KAMIN, Disappearance of phase in the Stefan problem: One space dimension, preprint 614, Institute for Mathematics and Its Applications, University of Minnesota, Minneapolis, 1990. S. B. ANGENENT AND J. J. L. VELÁZQUEZ, Degenerate neckpinches in mean curvature flow, J. Reine Angew. Math., to appear. A. BRESSAN, On the asymptotic shape of blow up, Indiana University Math. J., 39 (1990), pp. 947–959. A. BRESSAN, Stable blow up patterns, J. Differential Equations, 98 (1992), pp. 57–75. G. B. DAVIES AND J. M. HILL, A moving boundary problem for the sphere, IMA J. Appl. Math., 29 (1982), pp. 99–111. L. C. EVANS AND B. F. KNERR, Instantaneous shrinking of the support of nonnegative solutions to certain nonlinear parabolic equations and variational inequalities, Illinois J. Math., 23 (1979), pp. 153–166. Y. GIGA AND R. V. KOHN, Asymptotically self-similar blow up of semilinear heat equations, Comm. Pure Appl. Math., 38 (1985), pp. 297–319. J. M. HILL AND J. DEWYNNE, On an integral formulation for moving boundary problems, Quart. Appl. Math., XLI (1984), pp. 443–455. J. M. HILL AND J. DEWYNNE, On the inward solidification of cylinders, Quart. Appl. Math., XLIV (1986), pp. 59–70. M. A. HERRERO AND J. J. L. VELÁZQUEZ, Approaching an extinction point in one- dimensional semilinear heat equations with strong absorption, J. Math. Anal. Appl., 170 (1992), pp. 353–381. M. A. HERRERO AND J. J. L. VELÁZQUEZ, Singularity formulation in the one-dimensional supercooled Stefan problem, European J. Appl. Math., 7 (1996), pp. 119–150. M. A. HERRERO AND J. J. L. VELÁZQUEZ, Explosion de solutions d'equations paraboliques semilinéaires supercritiques, C. R. Acad. Sci. Paris Sér. I Math., 319 (1994), pp. 141–143. N. N. LEBEDEV, Special Functions and Their Applications, Dover, New York, 1972. A. M. MEIRMANOV, The Stefan Problem, Expositions in Mathematics Series, De Gruyter, Hawthorne, NY, 1992. P. M. MORSE AND H. FESHBACH, Methods of Theoretical Physics, Vol. I, McGraw–Hill, New York, 1953. L. I. RUBENSTEIN, The Stefan Problem, Transl. Math. Monographs 27, AMS, Providence, RI, 1971. D. S. RYLEY, F. T. SMITH, AND G. POOTS, The inward solidification of spheres and circular cylinders, Internat. J. Heat Mass Transfer, 17 (1974), pp. 1507–1516. A. M. SOWARD, A unified approach to Stefan's problem for spheres and cylinders, Proc. Royal Soc. London Ser. A, 373 (1980), pp. 131–147. K. STEWARTSON AND R. T. WAECHTER, On Stefan's problem for spheres, Proc. Royal Soc. London Ser. A, 348 (1976), pp. 415–526. | |
| dspace.entity.type | Publication |
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