zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Systems of p-Laplacian differential inclusions with large diffusion. (English) Zbl 1191.35163
Summary: We consider coupled systems of p-Laplacian differential inclusions and we prove, under suitable conditions, that a homogenization process occurs when diffusion parameters become arbitrarily large. In fact we obtain that the attractors are continuous at infinity on L 2 (Ω)×L 2 (Ω) topology, with respect to the diffusion coefficients, and the limit set is the attractor of an ordinary differential problem.

35K92Quasilinear parabolic equations with p-Laplacian
35R70PDE with multivalued right-hand sides
35K51Second-order parabolic systems, initial bondary value problems
35B41Attractors (PDE)
[1]Ball, J. M.: Continuity properties and global attractors of generalized semiflows and the Navier – Stokes equations, J. nonlinear sci. 7, No. 5, 475-502 (1997) · Zbl 0903.58020 · doi:10.1007/s003329900037
[2]Barbashin, E. A.: On the theory of general dynamical systems, Ucenye zapiski moskov. GoS univ. 135, 110-133 (1948)
[3]Brèzis, H.: Operateurs maximaux monotones et semi-groupes de contractions dans LES espaces de Hilbert, (1973)
[4]Brèzis, H.: Analyse fonctionnelle : théorie et applications, (1983) · Zbl 0511.46001
[5]Bridgland, T. F.: Contributions to the theory of generalized differential equations. I, II, Math. systems theory 3, 17-50 (1969) · Zbl 0179.12503 · doi:10.1007/BF01695624
[6]Bronstein, I. U.: Dynamical systems without uniqueness as semigroups of non-single-valued mappings of a topological space, Bul. akad. Stiince RSS moldoven. 1, 3-18 (1963)
[7]Budak, B. M.: The concept of motion in a generalized dynamical system, Moskov. GoS univ. Uc. zap. Mat. 155, No. 5, 174-194 (1952) · Zbl 0251.54024
[8]Carvalho, A. N.: Infinite dimensional dynamics described by ordinary differential equations, J. differential equations 116, 338-404 (1995) · Zbl 0847.34065 · doi:10.1006/jdeq.1995.1039
[9]Carvalho, A. N.; Gentile, C. B.: Asymptotic behaviour of non-linear parabolic equations with monotone principal part, J. math. Anal. appl. 280, No. 2, 252-272 (2003) · Zbl 1053.35027 · doi:10.1016/S0022-247X(03)00037-4
[10]Carvalho, A. N.; Hale, J. K.: Large diffusion with dispersion, Nonlinear anal. 17, No. 12, 1139-1151 (1991) · Zbl 0781.35028 · doi:10.1016/0362-546X(91)90233-Q
[11]Carvalho, A. N.; Piskarev, S.: A general approximation scheme for attractors of abstract parabolic problems, Numer. funct. Anal. optim. 27, No. 7 – 8, 785-829 (2006) · Zbl 1110.35012 · doi:10.1080/01630560600882723
[12]Conway, E.; Hoff, D.; Smoller, J.: Large time behavior of solutions of systems of non-linear reaction – diffusion equations, SIAM J. Appl. math. 35, 1 (1978) · Zbl 0383.35035 · doi:10.1137/0135001
[13]Díaz, J. I.; Hernandez, J.; Tello, L.: On the multiplicity of equilibrium solutions to a nonlinear diffusion equation on a manifold arising in climatology, J. math. Anal. appl. 216, 593-613 (1997) · Zbl 0892.35065 · doi:10.1006/jmaa.1997.5691
[14]Díaz, J. I.; Hetzer, G.; Tello, L.: An energy balance climate model with hysteresis, Nonlinear anal. 64, 2053-2074 (2006) · Zbl 1098.35090 · doi:10.1016/j.na.2005.07.038
[15]Díaz, J. I.; Schiavi, E.: On a degenerate parabolic/hyperbolic system in glaciology giving rise to a free boundary, Nonlinear anal. 38, 649-673 (1999) · Zbl 0935.35179 · doi:10.1016/S0362-546X(99)00101-7
[16]Díaz, J. I.; Vrabie, I. I.: Existence for reaction diffusion systems. A compactness method approach, J. math. Anal. appl. 188, 521-540 (1994) · Zbl 0815.35132 · doi:10.1006/jmaa.1994.1443
[17]Gentile, C. B.; Primo, M. R. T.: Parameter dependent quasi-linear parabolic equations, Nonlinear anal. 59, No. 5, 801-812 (2004)
[18]Hale, J. K.: Large diffusivity and asymptotic behavior in parabolic systems, J. math. Anal. appl. 118, 455-466 (1986) · Zbl 0602.35059 · doi:10.1016/0022-247X(86)90273-8
[19]Hale, J. K.; Rocha, C.: Varying boundary conditions with large diffusivity, J. math. Pures appl. 66, 139-158 (1987) · Zbl 0557.35078
[20]Hale, J. K.; Rocha, C.: Interaction of diffusion and boundary conditions, Nonlinear anal. 11, 633-649 (1987) · Zbl 0661.35047 · doi:10.1016/0362-546X(87)90078-2
[21]Kapustyan, A. V.; Melnik, V. S.: Global attractors of multivalued semidynamical systems and their approximations, Kibernet. sistem. Anal. 5, 102-111 (1998) · Zbl 0995.37011 · doi:10.1007/BF02667045
[22]Kapustyan, A. V.; Melnik, V. S.; Valero, J.; Yasinsky, V. V.: Global attractors of multivalued dynamical systems and evolution equations without uniqueness, monograph, (2008)
[23]Melnik, V. S.: Multivalued semiflows and their attractors, Dokl. akad. Nauk 343, No. 3, 302-305 (1995) · Zbl 0922.54035
[24]Melnik, V. S.; Valero, J.: On attractor of multivalued semi-flows and differential inclusions, Set-valued anal. 6, 83-111 (1998) · Zbl 0915.58063 · doi:10.1023/A:1008608431399
[25]Minkevič, M. I.: The theory of integral funnels in generalized dynamical systems without a hypothesis of uniqueness, Dokl. akad. Nauk SSSR (N.S.) 59, 1049-1052 (1948)
[26]Roxin, E.: On generalized dynamical systems defined by contingent equations, J. differential equations 1, 188-205 (1965) · Zbl 0135.30802 · doi:10.1016/0022-0396(65)90019-7
[27]Roxin, E.: Stability in general control systems, J. differential equations 1, 115-150 (1965) · Zbl 0143.32302 · doi:10.1016/0022-0396(65)90015-X
[28]Simsen, J.; Gentile, C. B.: On attractors for multivalued semigroups defined by generalized semiflows, Set-valued anal. 16, 105-124 (2008) · Zbl 1143.35310 · doi:10.1007/s11228-006-0037-1
[29]Simsen, J.; Gentile, C. B.: On p-Laplacian differential inclusions – global existence, compactness properties and asymptotic behavior, Nonlinear anal. 71, 3488-3500 (2009) · Zbl 1178.35208 · doi:10.1016/j.na.2009.02.044
[30]Simsen, J.; Gentile, C. B.: Well-posed p-Laplacian problems with large diffusion, Nonlinear anal. 71, 4609-4617 (2009) · Zbl 1167.35405 · doi:10.1016/j.na.2009.03.041
[31]Szego, G. P.; Treccani, G.: Semigruppi di transformazioni multivoche, Lecture notes in math. 101 (1969) · Zbl 0286.34073
[32]Temam, R.: Infinite-dimensional dynamical systems in mechanics and physics, (1988)