Linear and semilinear higher order parabolic equations in R-N
| dc.contributor.author | Rodríguez Bernal, Aníbal | |
| dc.contributor.author | Cholewa, Jan W. | |
| dc.date.accessioned | 2023-06-20T00:22:29Z | |
| dc.date.available | 2023-06-20T00:22:29Z | |
| dc.date.issued | 2010-01 | |
| dc.description.abstract | In this paper we consider some fourth order linear and semilinear equations in R-N and make a detailed study of the solvability of the Cauchy problem. For the linear equation we consider some weakly integrable potential terms, and for any 1 < p < infinity prove that for a suitable family of Bessel potential spaces, H-p(alpha) (R-N), the linear equation defines a strongly continuous analytic semigroup. Using this result, we prove that the nonlinear problems we consider can be solved for initial data in L-p(RN) and in H-p(2) (R-N). We also find the corresponding critical exponents, that is, the largest growth allowed for the nonlinear terms for these classes of initial data. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | MEC | |
| dc.description.sponsorship | UCM, Spain | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/17660 | |
| dc.identifier.doi | 10.1016/j.na.2011.08.022 | |
| dc.identifier.issn | 0362-546X | |
| dc.identifier.officialurl | http://www.sciencedirect.com/science/article/pii/S0362546X1100575X | |
| dc.identifier.relatedurl | http://www.sciencedirect.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/42474 | |
| dc.issue.number | 1 | |
| dc.journal.title | Nonlinear Analysis: Theory, Methods & Applications | |
| dc.language.iso | eng | |
| dc.page.final | 210 | |
| dc.page.initial | 194 | |
| dc.publisher | Elsevier | |
| dc.relation.projectID | GR58/08 Grupo 920894 | |
| dc.relation.projectID | MTM2009-07540 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 517.986 | |
| dc.subject.keyword | Interpolation spaces | |
| dc.subject.keyword | Fractional powers of operators | |
| dc.subject.keyword | Analytic semigroups | |
| dc.subject.keyword | Initial value problems for higher order parabolic equations | |
| dc.subject.keyword | Semilinear parabolic equations | |
| dc.subject.keyword | Critical exponents | |
| dc.subject.keyword | Critical Nonlinearities | |
| dc.subject.ucm | Funciones (Matemáticas) | |
| dc.subject.unesco | 1202 Análisis y Análisis Funcional | |
| dc.title | Linear and semilinear higher order parabolic equations in R-N | |
| dc.type | journal article | |
| dc.volume.number | 75 | |
| dcterms.references | H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, Veb Deutscher, Berlin, 1978. J.M. Arrieta, J.W. Cholewa, T. Dlotko, A. Rodriguez-Bernal, Linear parabolic equations in locally uniform spaces, Math. Models Methods Appl. Sci. 14 (2004) 253–294. T. Kato, The Cauchy problem for quasi-linear symmetric hyperbolic systems, Arch. Ration. Mech. Anal. 58 (1975) 181–205. H. Amann, M. Hieber, G. Simonnett, Bounded H∞ calculus for elliptic operators, Differential Integral Equations 7 (1994) 613–653. H. Amann, Linear and Quasilinear Parabolic Problems, Birkhäuser, Basel, 1995. D. Henry, Geometric Theory of Semilinear Parabolic Equations, in: Lecture Notes in Mathematics, vol. 840, Springer, Berlin, 1981. A.N. Carvalho, J.W. Cholewa, Continuation and asymptotics of solutions to semilinear parabolic equations with critical nonlinearities, J. Math. Anal. Appl. 310 (2005) 557–578. J.M. Arrieta, A.N. Carvalho, Abstract parabolic problems with critical nonlinearities and applications to Navier–Stokes and heat equations, Trans. Amer. Math. Soc. 352 (2000) 285–310. J.W. Cholewa, A. Rodriguez-Bernal, Dissipative mechanism of a semilinear higher order parabolic equation in RN . Serie de Prepublicaciones del Departamento de Matematica Aplicada, U. Complutense, MA-UCM 2011-13. http://www.mat.ucm.es/deptos/ma. H. Komatsu, Fractional powers of operators, Pacific J. Math. 19 (1966) 285–346. J.W. Cholewa, T. Dlotko, Global Attractors in Abstract Parabolic Problems, Cambridge University Press, Cambridge, 2000. A. Rodriguez-Bernal, Perturbation of analytic semigroups in scales of Banach spaces and applications to parabolic equations with low regularity data, SEMA J. 53 (2011) 3–54. J.M. Arrieta, J.W. Cholewa, T. Dlotko, A. Rodriguez-Bernal, Asymptotic behavior and attractors for reaction diffusion equations in unbounded domains, Nonlinear Anal. TMA 56 (2004) 515–554. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, Berlin, 1983 | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | fb7ac82c-5148-4dd1-b893-d8f8612a1b08 | |
| relation.isAuthorOfPublication.latestForDiscovery | fb7ac82c-5148-4dd1-b893-d8f8612a1b08 |
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