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On the behavior of the solutions of certain nonlinear parabolic problems (Spanish: Sobre el comportamiento de las soluciones de ciertos problemas parabólicos no lineales)

dc.contributor.authorHerrero, Miguel A.
dc.date.accessioned2023-06-21T02:06:40Z
dc.date.available2023-06-21T02:06:40Z
dc.date.issued1981
dc.description.abstractFor 1<p<∞ let Δpu=∑ni=1Dxi(|Dxiu|p−2Dxiu). Consider the initial value problem (∗) ut−Δpu+β(u)=0 for (x,t)∈Rn×[0,T], u(0)=u0(x) for x∈Rn. Here β is a continuous, nondecreasing real function such that β(0)=0. The author obtains sufficient conditions for the existence of both finite extinction time and compact support in x for solutions of (∗). Some counterexamples are given when the conditions are removed.
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.description.refereedTRUE
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/22782
dc.identifier.citationBAMBERGER, A. (1977). Étude d'une équation doublement non linéaire. Journal of Functional Analysis, 24, 148-155. BENILAN, PH. (1972). Équations d'évolution dans un espace de Banach quelconque et applications. Thèse d'Etat, Orsay. BENILAN, PH. (1975). Cours de 3eme cycle, Paris. BENILAN, PH., BREZIS, H. y CRANDALL, M. (1975). A semilinear equation in L1 (RN). Ann. Ecuola Normale Superiore di Pisa, serie IV, vol. II, 4, 523-555. BENILAN, PH. y PICARD, C. (1974). Quelques aspects non linéaires de la théorie du potentiel. Séminaire Théorie du potential, Paris VI. BREZIS, H. (1973). Operateurs maximaux monotones et semigroupes de contractions dans les espaces de Hilbert. Notas de Matemática, North Holland. BREZIS, H. (1971). Monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations, en Contributions to nonlinear functional analysis. E. Zarantonello, ed. BREZIS, H . (1974). Solutions of variational inequalities with compact support. Uspekhi Mat, Nauk., 129, 103-108. BREZIS, H . (1974). Monotone operators, nonlinear semigroups and applications. Proc. Int. Congress. Math. Vancouver, Canadá. BREZIS, H . y FRIEDMAN, A. (1976). Estimates on the support of solutions of parabolic variational inequalities. III. Journal of Math., 20, 82-99. DÍAZ, G. y DÍAZ, J. I. (1979). Finite extinction time for a class of nonlinear parabolic equations. Comm, in Partial Differential Equations, 4, 11, 1213-1231. DÍAZ, J. I. (1979). Solutions with compact support of some degenerate parabolic problems. Nonlinear Analysis. Theory and Applications, vol. 3, 6, 831-847. DÍAZ, J. I. y HERRERO, M. A. Estimates on the support of the solutions of some nonlinear elliptic and parabolic problems (aparecerá enroceedings of the Royal Society of Edinburgh). EVANS, L . C. y KNERR, B . F . (1979). Instantaneous shrinking of the support of non-negative solutions to certain nonlinear parabolic equations and variational inequalities. III. J. of Math., 23, 1, 153-166. HERRERO, M. A. (1979). Comportamiento de las soluciones de ciertos problemas no lineales sobre dominios no acotados. Tesis doctoral. Universidad Complutense, Madrid. LIONS, J. L. (1969). Quelques méthodes de résolution des problèmes aux limites non linéaires. Ed. Dunod. KALASHNIKOV, A. S. (1973). On the Cauchy problem in the class of increasing functions for certain quasilinear degenerate parabolic equations of the second order. Differentialnye urav. Tom. IX, n.º 4, 682-691 (en ruso). KALASHNIKOV, A. S. (1974). The propagation of disturbances in problems of nonlinear heat conduction with absorption. Zh. vychisl. Mat mat. Fiz,, 14, 4, 891-905. KALASHNIKOV, A. S. (1978). On a nonlinear equation arising in the theory of nonstationary filtration. Sem. I. G. Petrovski, en ruso. MARTINSON, L. K. y PAULOV, K. B . (1966). The effect of magnetic plasticity in non-newtonian fluids. Magnitaya Gidrodinamika, vol. 2, 3, 69-75. MARTINSON, L. K. y PAULOV, K. B . (1971). Unsteady shear flows of a conducting fluid with a rheological power law. Magnitaya Gidrodinamika, 2, 50-58. STAMPACCHIA, G. (1966). Equations elliptiques du second ordre a coefficients discontinus. Presses de l'Université de Montreal.
dc.identifier.issn0034-0596
dc.identifier.officialurlhttp://dmle.cindoc.csic.es/revistas/detalle.php?numero=5527
dc.identifier.relatedurlhttp://dmle.cindoc.csic.es/
dc.identifier.relatedurlhttp://www.rac.es/0/0_1.php
dc.identifier.urihttps://hdl.handle.net/20.500.14352/64876
dc.issue.number5
dc.journal.titleRevista de la Real Academia de Ciencias Exactas, Físicas y Naturales de Madrid
dc.language.isospa
dc.page.final1183
dc.page.initial1165
dc.publisherReal Academia de Ciencias Exactas, Físicas y Naturales
dc.rights.accessRightsrestricted access
dc.subject.cdu517.9
dc.subject.cdu517.956.4
dc.subject.ucmEcuaciones diferenciales
dc.subject.unesco1202.07 Ecuaciones en Diferencias
dc.titleOn the behavior of the solutions of certain nonlinear parabolic problems (Spanish: Sobre el comportamiento de las soluciones de ciertos problemas parabólicos no lineales)
dc.typejournal article
dc.volume.number75
dspace.entity.typePublication
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