New Results on the Burgers and the Linear Heat Equations in
Unbounded Domains
| dc.contributor.author | Díaz Díaz, Jesús Ildefonso | |
| dc.contributor.author | González, S. | |
| dc.date.accessioned | 2023-06-20T10:54:22Z | |
| dc.date.available | 2023-06-20T10:54:22Z | |
| dc.date.issued | 2005 | |
| dc.description.abstract | We consider the Burgers equation and prove a property which seems to have been unobserved until now: there is no limitation on the growth of the nonnegative initial datum u0(x) at infinity when the problem is formulated on unbounded intervals, as, e.g. (0 + ∞), and the solution is unique without prescribing its behaviour at infinity. We also consider the associate stationary problem. Finally, some applications to the linear heat equation with boundary conditions of Robin type are also given. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | DGISPI (Spain) | |
| dc.description.sponsorship | EU | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/30659 | |
| dc.identifier.issn | 1578-7303 | |
| dc.identifier.officialurl | http://www.rac.es/ficheros/doc/00177.pdf | |
| dc.identifier.relatedurl | http://www.springer.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/51426 | |
| dc.issue.number | 2 | |
| dc.journal.title | Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas | |
| dc.language.iso | eng | |
| dc.page.final | 225 | |
| dc.page.initial | 219 | |
| dc.publisher | Springer | |
| dc.relation.projectID | MTM2004–07590–C03–01 | |
| dc.relation.projectID | RTN HPRN–CT–2002–00274 | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 517.9 | |
| dc.subject.keyword | Viscous Burgers equation | |
| dc.subject.keyword | linear heat equation | |
| dc.subject.keyword | Robin boundary conditions | |
| dc.subject.keyword | stationary Burgers equation | |
| dc.subject.ucm | Ecuaciones diferenciales | |
| dc.subject.unesco | 1202.07 Ecuaciones en Diferencias | |
| dc.title | New Results on the Burgers and the Linear Heat Equations in Unbounded Domains | |
| dc.type | journal article | |
| dc.volume.number | 99 | |
| dcterms.references | Bandle, C., Díaz, G. and Díaz, J. I. (1994). Solutions d’equations de reaction diffusion nonlineaires, exploxant au bord parabolic. Comptes Rendus Acad. Sci. Paris, 318, Serie I, 455–460. Bernis, F. (1989). Elliptic and parabolic semilinear problems without conditions at infinity, Archive for Rational Mechanics and Analysis, 106, 3, 217–241. Boccardo, L., Gallouet, T. and Vázquez, J. L. Solutions of nonlinear parabolic equations without growth restric- ´ tions on the data, Electronic Journal Differential Equations, 2001. (URL http://ejde.math.swt.edu o http://ejde.math.unt.edu) Brauner, C.-M. (2005). Some models of cellular flames: Lecture at the Summer School.”Fronts and singularities: mathematics for other sciences”, El Escorial, Madrid. July 11–15, Brezis, H. (1984). Semilinear equations in RN without condition at infinity, Appl. Math. Optim., 12, 3, 271–282. Díaz, G. and Letelier, R. (1993). Explosive solutions of quasilinear elliptic equations: Existence and uniqueness, Nonlinear Anal. T.M.A., 20, 97–125. Díaz, J. I. (1991). Sobre la controlabilidad aproximada de problemas no lineales disipativos. In Jornadas Hispano Francesas sobre Control de Sistemas Distribuidos. Univ. de Malaga, 41–49. Díaz, J. I. and González, S. (2005). On the Burgers' equation in unbounded domains without condition at infinity, Proceeddings of the XIX CEDYA, Univ. Carlos III, Leganes, Madrid, 19-23 Septiembre de 2005. Díaz, J. I. and González, S. Paper in preparation. Díaz, J. I. and Oleinik, O. A. (1992). Nonlinear elliptic boundary value problems in unbounded domains and the asymptotic behaviour of its solutions. Comptes Rendus Acad. Sci. Paris, 315, Serie I, 787–792. Díaz, J. I. (1995). Obstruction and some approximate controllability results for the Burgers' equation and related problems. In Control of partial differential equations and applications (E. Casas ed.), Lecture Notes in Pure and Applied Mathematics, 174, Marcel Dekker, Inc., New York, 63–76. Fernández de la Mora, J. (2004). The spreading of a charged cloud, Burgers’equation, and nonlinear simple waves in a perfect gas, In Simplicity, Rigor and Relevance in Fluid Mechanics, F. J. Higuera et al eds. CIMNE, Barcelona, 250–266. Herrero, M. A. and Pierre, M. (1985). Some results for the Cauchy problem for ut = ∆u m when 0 < m < 1,Trans. A. M. S., 291, 145–158. Porretta, A. (2002).Uniqueness of solutions of some elliptic equations without condition at infinity, C.R.Acad. Sci. Paris, Ser. I, 335, 739–744. Strauss, W. A. (1992). Partial Differential Equations. John Wiley & Sons, New York. Witham, G. B. (1974). Linear and nonlinear waves, Wiley Interscience, New York. Yamada, K. (2005). On viscous conservation laws growing initial data, Differential and Integral Equations, 18,8, 841–854. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 34ef57af-1f9d-4cf3-85a8-6a4171b23557 | |
| relation.isAuthorOfPublication.latestForDiscovery | 34ef57af-1f9d-4cf3-85a8-6a4171b23557 |
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