Multivalued dynamics of solutions of an autonomous differential-operator inclusion with pseudomonotone nonlinearity. (English. Russian original) Zbl 1300.47084
Cybern. Syst. Anal. 47, No. 5, 800-811 (2011); translation from Kibern. Sist. Anal. 2011, No. 5, 150-163 (2011).
Summary: This article considers a nonlinear autonomous differential-operator inclusion with a pseudomonotone dependence between determinative problem parameters. The dynamics of all weak solutions defined on the positive semi-axis of time is studied. The existence of trajectory and global attractors is proved and their structure is investigated. A class of high-order nonlinear parabolic equations is considered to be a possible application.
MSC:
| 47J22 | Variational and other types of inclusions |
| 34A60 | Ordinary differential inclusions |
| 47N20 | Applications of operator theory to differential and integral equations |
| 35K25 | Higher-order parabolic equations |
| 35K55 | Nonlinear parabolic equations |
Keywords:
differential-operator inclusion; global attractor; trajectory attractor; pseudomonotone mappingReferences:
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