Existence and invariance of global attractors for impulsive parabolic system without uniqueness. (English) Zbl 1416.35045
Sadovnichiy, Victor A. (ed.) et al., Modern mathematics and mechanics. Fundamentals, problems and challenges. Cham: Springer. Underst. Complex Syst., 57-78 (2019).
Summary: In this paper, we apply the abstract theory of global attractors for multi-valued impulsive dynamical systems to weakly-nonlinear impulsively perturbed parabolic system without uniqueness of a solution to the Cauchy problem. We prove that for a sufficiently wide class of impulsive perturbations (including multi-valued ones) the global attractor of the corresponding multi-valued impulsive dynamical system has an invariant non-impulsive part.
For the entire collection see [Zbl 1411.00047].
For the entire collection see [Zbl 1411.00047].
MSC:
| 35B41 | Attractors |
| 35R12 | Impulsive partial differential equations |
| 35K10 | Second-order parabolic equations |
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