Long-time behavior for a class of extensible beams with nonlocal weak damping and critical nonlinearity
Chunxiang Zhao, Shan Ma, Chengkui Zhong
Abstract
This paper is devoted to establishing the long-time behavior of extensible beam equation with the nonlocal weak damping on a bounded smooth domain of Rn with hinged (clamped) boundary condition. It proves the well-posedness by means of the monotone operator theory and the existence of a global attractor when the growth exponent of the nonlinearity f(u) is up to the critical case in natural energy space.
Topics & Concepts
Bounded functionDomain (mathematical analysis)Nonlinear systemAttractorBoundary value problemMathematical analysisBoundary (topology)Monotone polygonMathematicsClass (philosophy)Critical exponentOperator (biology)Beam (structure)PhysicsQuantum mechanicsGeometryScalingComputer scienceTranscription factorGeneChemistryRepressorBiochemistryOpticsArtificial intelligenceStability and Controllability of Differential EquationsAdvanced Mathematical Physics ProblemsAdvanced Mathematical Modeling in Engineering