Regularity of Euler-Bernoulli and Kirchhoff-Love Thermoelastic Plates with Fractional Coupling

2022/09/19 by Suárez, Fredy Maglorio Sobrado, Sobrado, Lesly Daiana Barbosa
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2209.08695

Abstract

I In this work, we present the study of the regularity of the solutions of the abstract system\eqrefEq1.10 that includes the Euler-Bernoulli(ω=0) and Kirchoff-Love(ω>0) thermoelastic plates, we consider for both fractional couplings given by A^σθ and A^σu_t, where A is a strictly positive and self-adjoint linear operator and the parameter σ∈[0,(3)/(2)]. Our research stems from the work of \citeMSJR, \citeOroJRPata2013, and \citeKLiuH2021. Our contribution was to directly determine the Gevrey sharp classes: for ω=0, s₀₁>(1)/(2σ-1) and s₀₂> σ when σ∈ ((1)/(2),1) and σ∈ (1,(3)/(2)) respectively. And s_ω>(1)/(4(σ-1)) for case ω>0 when σ∈ (1,(5)/(4)). This work also contains direct proofs of the analyticity of the corresponding semigroups e^t\mathbbA_ω: In the case ω=0 the analyticity of the semigroup e^t\mathbbA₀ occurs when σ=1 and for the case ω>0 the semigroup e^t\mathbbA_ω is analytic for the parameter σ∈[5/4, 3/2]. The abstract system is given by: \u_tt+ωAu_tt+A²u-A^σθ=0,
θ_t+Aθ+A^σu_t=0.. where ω≥ 0.

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