Long-time dynamical behavior for a piezoelectric system with magnetic effect and nonlinear dampings

DOI10.3934/era.2022173OpenAlexW4225949825MaRDI QIDQ2700274

Gongwei Liu, Pengyan Ding, Mengru Wang

Publication date: 20 April 2023

Published in: Electronic Research Archive (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2203.16736

zbMATH Keywords

piezoelectric systemglobal attractorwell posednessexponential attractorsupper semicontinuity of attractors

Mathematics Subject Classification ID

Dynamical systems and ergodic theory (37-XX) Partial differential equations (35-XX)

Cites Work

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• Further stabilization and exact observability results for voltage-actuated piezoelectric beams with magnetic effects
• Finite dimensionality and regularity of attractors for a 2-D semilinear wave equation with nonlinear dissipation
• Lower semicontinuity of attractors of gradient systems and applications
• Uniform boundary stabilization of the finite difference space discretization of the 1-D wave equation
• Long-time dynamics of a coupled system of nonlinear wave and thermoelastic plate equations
• Semigroups of linear operators and applications to partial differential equations
• Compact sets in the space \(L^ p(0,T;B)\)
• Upper semicontinuity of the attractor for a singularly perturbed hyperbolic equation
• Two questions concerning the boundary control of certain elastic systems
• Representation of solutions and stability of linear differentialdifference equations in a Banach space
• Infinite-dimensional dynamical systems in mechanics and physics.
• Continuous dependence of attractors on the shape of domain
• Exponential stabilization of fully dynamic and electrostatic piezoelectric beams with delayed distributed damping feedback
• Quasi-stability and continuity of attractors for nonlinear system of wave equations
• Stabilization results for well-posed potential formulations of a current-controlled piezoelectric beam and their approximations
• Existence and continuity of global attractors for ternary mixtures of solids
• Dynamics of piezoelectric beams with magnetic effects and delay term
• Attractors for semilinear wave equations with localized damping and external forces
• Equivalence between exponential stabilization and boundary observability for piezoelectric beams with magnetic effect
• Asymptotic analysis and upper semicontinuity with respect to rotational inertia of attractors to von Karman plates with geometrically localized dissipation and critical nonlinearity
• Decay rates for Bresse system with arbitrary nonlinear localized damping
• Local and global well-posedness of semilinear Reissner-Mindlin-Timoshenko plate equations
• Long-time dynamics for a fractional piezoelectric system with magnetic effects and Fourier's law
• Modeling and Stabilizability of Voltage-Actuated Piezoelectric Beams with Magnetic Effects
• On the continuity of global attractors
• Von Karman Evolution Equations
• An Example on the Effect of Time Delays in Boundary Feedback Stabilization of Wave Equations
• Not All Feedback Stabilized Hyperbolic Systems are Robust with Respect to Small Time Delays in Their Feedbacks
• Exponential stability and numerical treatment for piezoelectric beams with magnetic effect
• Smart Material Systems
• ON THE ATTRACTOR FOR A SEMILINEAR WAVE EQUATION WITH CRITICAL EXPONENT AND NONLINEAR BOUNDARY DISSIPATION
• Nonlinear Differential Equations of Monotone Types in Banach Spaces

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