Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 1018.37048
Caraballo, T.; Langa, J.A.; Melnik, V.S.; Valero, J.
Pullback attractors of nonautonomous and stochastic multivalued dynamical systems.
(English)
[J] Set-Valued Anal. 11, No.2, 153-201 (2003). ISSN 0927-6947; ISSN 1572-932X/e

The existence of pullback global attractors for multivalued processes generated by differential inclusions is studied. Mainly one deals with nonautonomous multivalued dynamical systems in which the trajectories can be unbounded in time and with nonautonomous stochastic multivalued dynamical systems. Let $X$ be a complete metric space, $P(X)$ the set of all subsets of $X$. Denote $\bbfR_d= \{(t,s)\in \bbfR^z:t\ge s\}$. The map $U:\bbfR_d\times X \to P(X)$ is called a multivalued dynamical process (MDP) on $X$ if 1) $U(t,t, \cdot)$ is the identical map, 2) $U(t,s,x)\subset U(t,\tau,U (\tau,s,x))$, $x\in X$, $s<\tau <t$.\par At first the authors proved abstract results on the existence of $\omega$-limit sets and global attractors and studied their topological properties (compactness, connectedness). Then they applied the abstract results to nonautonomous differential inclusions of the reaction-diffusion type in which the forcing term can grow polynomially in time and they gave applications to stochastic differential inclusions with additive and multiplicative noises. MDP is defined as a two-parameter family of multivalued maps. The attraction of any bounded set of the phase space to the global attractor is uniform with respect to the first parameter. The rate of attraction and the attractor itself can depend on the second parameter. The theory is extended to the cases with stochastic terms in the model.
MSC 2000:
*37L55 Infinite-dimensional random dynamical systems etc.
35B41 Attractors
35K55 Nonlinear parabolic equations
35K57 Reaction-diffusion equations

Keywords: $\omega$-limit sets; attractor; differential inclusion; reaction-diffusion equation; nonautonomous dynamical system

Highlights
Master Server