Long-time dynamics for a fractional piezoelectric system with magnetic effects and Fourier's law

DOI10.1016/j.jde.2021.01.030zbMath1459.35038OpenAlexW3127083637MaRDI QIDQ2656306

A. J. A. Ramos, Mirelson M. Freitas, Ahmet Özkan Özer, D. S. Almeida Júnior

Publication date: 11 March 2021

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2021.01.030

zbMATH Keywords

global attractorsFourier lawfractional dampingparabolic-hyperbolic systemupper-semicontinuitythermo-piezo-magnetic beam

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Asymptotic behavior of solutions to PDEs (35B40) Attractors (35B41) Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems (37L30) Thermodynamics in solid mechanics (74A15) Thermal effects in solid mechanics (74F05) Electromagnetic effects in solid mechanics (74F15) Fractional partial differential equations (35R11)

Related Items (19)

Regularity and upper semicontinuity of pullback attractors for non-autonomous Rao–Nakra beam ⋮ Global attractors for a novel nonlinear piezoelectric beam model with dynamic electromagnetic effects and viscoelastic memory ⋮ Stability of multi-dimensional nonlinear piezoelectric beam with viscoelastic infinite memory ⋮ Exponential stabilization of piezoelectric beams with magnetic effect and second sound ⋮ Longtime dynamics for a novel piezoelectric beam model with creep and thermo-viscoelastic effects ⋮ Equivalence between exponential stabilization and observability inequality for magnetic effected piezoelectric beams with time-varying delay and time-dependent weights ⋮ Stability and Eigenvalue Asymptotics of Multi-Dimensional Fully Magnetic Effected Piezoelectric System with Friction-Type Infinite Memory ⋮ Stability results for piezoelectric beams with long‐range memory effects in the boundary ⋮ General stability for piezoelectric beams with a nonlinear damping term ⋮ Stabilization of nonlinear non-uniform piezoelectric beam with time-varying delay in distributed control input ⋮ Global well-posedness and exponential decay of fully dynamic and electrostatic or quasi-static piezoelectric beams subject to a neutral delay ⋮ Existence and robustness results of attractors for partially-damped piezoelectric beams ⋮ Existence and continuity of attractors for a nonlinear piezoelectric beam with Colemam-Gurtin thermal law ⋮ Long-time dynamical behavior for a piezoelectric system with magnetic effect and nonlinear dampings ⋮ Unnamed Item ⋮ Robustness of global attractors for extensible coupled suspension bridge equations with fractional damping ⋮ Stabilization results for well-posed potential formulations of a current-controlled piezoelectric beam and their approximations ⋮ Attractors and pullback dynamics for non-autonomous piezoelectric system with magnetic and thermal effects ⋮ Exponential stability for magnetic effected piezoelectric beams with time-varying delay and time-dependent weights

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Rate of attraction for a semilinear wave equation with variable coefficients and critical nonlinearities
• Further stabilization and exact observability results for voltage-actuated piezoelectric beams with magnetic effects
• Exponential decay in a thermoelastic mixture of solids
• Characterization of domains of fractional powers of certain operators arising in elastic systems, and applications
• Strongly damped wave problems: bootstrapping and regularity of solutions
• Semigroups of linear operators and applications to partial differential equations
• Proof of extensions of two conjectures on structural damping for elastic systems
• Upper semicontinuity of the attractor for a singularly perturbed hyperbolic equation
• Geometric theory of semilinear parabolic equations
• Regularity of some structurally damped problems with point control and with boundary control
• Exact null controllability of structurally damped and thermoelastic parabolic models
• On the exponential decay of the energy of a linear thermoelastic plate
• Exponential stability and analyticity of abstract linear thermoelastic systems
• Null-controllability of a system of linear thermoelasticity
• Attractors and their stability on Boussinesq type equations with gentle dissipation
• Criteria on the existence and stability of pullback exponential attractors and their application to non-autonomous Kirchhoff wave models
• Continuity of non-autonomous attractors for hyperbolic perturbation of parabolic equations
• Stability of exponential attractors for a family of semilinear wave equations with gentle dissipation
• Decay rates for the three-dimensional linear system of thermoelasticity
• Mildly dissipative nonlinear Timoshenko systems -- global existence and exponential stability.
• Attractors for strongly damped wave equations with critical nonlinearities.
• A note on the equations of a thermoelastic plate
• Large solutions and smoothing properties for nonlinear thermoelastic systems
• Exponential stabilization of fully dynamic and electrostatic piezoelectric beams with delayed distributed damping feedback
• Fractional Schrödinger equation; solvability and connection with classical Schrödinger equation
• Upper semicontinuity of global attractors for a family of semilinear wave equations with gentle dissipation
• Regularity of solutions on the global attractor for a semilinear damped wave equation
• A general theory of heat conduction with finite wave speeds
• Structurally damped elastic waves in 2D
• Modeling and Stabilizability of Voltage-Actuated Piezoelectric Beams with Magnetic Effects
• Rates of decay to weak thermoelastic Bresse system
• Von Karman Evolution Equations
• On the Energy Decay of a Linear Thermoelastic Bar and Plate
• Analyticity, and lack thereof, of thermo-elastic semigroups
• Exponential stability of the Kirchhoff plate with thermal or viscoelastic damping
• Modeling and Controlling an Active Constrained Layer (ACL) Beam Actuated by Two Voltage Sources With/Without Magnetic Effects
• Smart Material Systems
• ON THE ATTRACTOR FOR A SEMILINEAR WAVE EQUATION WITH CRITICAL EXPONENT AND NONLINEAR BOUNDARY DISSIPATION
• Local well posedness for strongly damped wave equations with critical nonlinearities
• Smoothing Properties, Decay, and Global Existence of Solutions to Nonlinear Coupled Systems of Thermoelastic Type
• Dissipative periodic processes
• Singular Limit and Long-Time Dynamics of Bresse Systems
• Gevrey Class Semigroups Arising from Elastic Systems with Gentle Dissipation: The Case 0 < α < ½

This page was built for publication: Long-time dynamics for a fractional piezoelectric system with magnetic effects and Fourier's law