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)
Dynamics of the nonclassical diffusion equations. (English) Zbl 1154.35063

The authors consider the long-time behaviour of the solutions for a nonclassical diffusion equation used in fluid mechanics, solid mechanics and heat conduction theory.

It is different from the usual reaction diffusion equation, consequently it is possible to use the compact Sobolev embedding to obtain the key asymptotic compactness for both autonomous and nonautonomous cases.

For the autonomous case Sun and Yang prove by a decomposition technique the existence of a global attractor in H 0 1 only assuming that the forcing term is in H -1 ·

For the nonhomogeneous case under hypotheses that the forcing term is translation bounded is established that asymptotically the solutions are exponentially closing on approaching more regular solutions. As a consequence is proved the existence of a compact uniform attractor and moreover the existence of nonautonomous exponential attractors.


MSC:
35K70Ultraparabolic equations, pseudoparabolic equations, etc.