Regularity of the Timoshenko’s System with Thermoelasticity of Type III and Fractional Damping

• DOI: 10.22533/at.ed.3742302081

• Palavras-chave: --

• Keywords: Gevrey class, Analyticity, Fractional damping, Semigroup theory

• Abstract:

  The article presents the study of the regularity of two thermoelastic beam systems defined by the Timoshenko beam model coupled with the heat conduction of Green-Naghdiy theory of type III, both mathematical models are differentiated by their coupling terms that arise as a consequence of the constitutive laws initially considered. The systems presented in this work have 3 fractional dampings: μ1(−Δ)τϕt, μ2(−Δ)σψt and K(−Δ)ξθt, where ϕ, ψ and θ are transverse displacement, rotation angle and empirical temperature of the bean respectively and the parameters (τ, σ, ξ) ∈ [0, 1]3. It is noted that for values 0 and 1 of the parameter τ , the so-called frictional or viscous damping will be faced, respectively.