Dynamics of piezoelectric beams with magnetic effects and delay term
Mirelson M. Freitas, A. J. A. Ramos, M. J. Dos Santos, J.L.L. Almeida
Abstract
<p style='text-indent:20px;'>In this paper, we consider a piezoelectric beams system with magnetic effects and delay term. We study its long-time behavior through the associated dynamical system. We prove that the system is gradient and asymptotically smooth, which as a consequence, implies the existence of a global attractor, which is characterized as unstable manifold of the set of stationary solutions. We also get the quasi-stability of the system by establishing a stabilizability estimate and therefore obtain the finite fractal dimension of the global attractor.</p>
Topics & Concepts
AttractorTerm (time)Stability (learning theory)Manifold (fluid mechanics)PhysicsFractal dimensionMathematical analysisDimension (graph theory)Set (abstract data type)Dynamical system (definition)MathematicsFractalDynamical systems theoryApplied mathematicsStatistical physicsPure mathematicsComputer scienceQuantum mechanicsMechanical engineeringMachine learningProgramming languageEngineeringStability and Controllability of Differential EquationsAdvanced Mathematical Modeling in EngineeringNonlinear Dynamics and Pattern Formation