zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
Global attractors for a nonclassical diffusion equation. (English) Zbl 1128.35027

Summary: We prove the existence of global attractors in H 0 1 (Ω) for a nonclassical diffusion equation

u t -Δu t -Δu=f(u)+D i f i +g(x)inΩ·

Two types of nonlinearity f are considered: one is the critical exponent, and the other is the polynomial growth of arbitrary order.

MSC:
35B41Attractors (PDE)
35Q35PDEs in connection with fluid mechanics
35B40Asymptotic behavior of solutions of PDE
References:
[1]Aifantis, E. C.: On the problem of diffusion in solids. Acta Mech., 37, 265–296 (1980) · Zbl 0447.73002 · doi:10.1007/BF01202949
[2]Lions, J. L., Magenes, E.: Non-homogeneous boundary value problems and appliations, Spring-Verlag, Berlin, 1972
[3]Peter, J. G., Gurtin, M. E.: On the theory of heat condition involving two temperatures. Z. Ange. Math. Phys., 19, 614–627 (1968) · Zbl 0159.15103 · doi:10.1007/BF01594969
[4]Zhong, C. K., Yang, M. H., Sun, C. Y.: The existence of global attractors for the norm-to-weak continuous semigroup and its application to the nonlinear reaction-diffusion equations. J. Differential Equations, 223, 367–399 (2006) · Zbl 1101.35022 · doi:10.1016/j.jde.2005.06.008
[5]Babin, A. V., Vishik, M. I.: Attractors of evolution equations, North-Holland, Amsterdam, 1992
[6]Cholewa, J. W., Dlotko, T.: Bi-spaces global attractors in abstract parabolic equations. Evol. Equations, Banach Center Publications, 60, 13–26 (2003) · doi:10.4064/bc60-0-1
[7]Ma, Q. F., Wang, S. H., Zhong, C. K.: Necessary and sufficient conditions for the existence of global attractors for semigroups and applications. J. Indiana University Math., 51(6), (2002)
[8]Xiao, Y. L.: Attractors for a nonclassical diffusion equation. Actc Mathematicae Applicatae Sinca, English Series, 18(1), 273–276 (2002) · Zbl 1017.35025 · doi:10.1007/s102550200026
[9]Cholewa, J. W., Dlotko, T.: Global attractors in abstract parabolic problems, Cambridge University Press, Cambridge, 2000
[10]Hale, J. K.: Asymptotic behavior of dissipative systems, AMS, Providence, RJ, 1988
[11]Temam, R.: Infinite-dimensional dynamical systems in mechanics and physics, Springer, New York, 1997
[12]Sun, C. Y., Zhong, C. K.: Attractors for the semilinear reaction-diffusion equation with distribution derivatives in unbounded domains. Nonl. Anal., 63, 49–65 (2005) · Zbl 1082.35036 · doi:10.1016/j.na.2005.04.034