A Gevrey class semigroup, exponential decay and Lack of analyticity for a system formed by a Kirchhoff-Love plate equation and the equation of a membrane-like electric network with indirect fractional damping
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| Formato: | Preprint |
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2019
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| _version_ | 1866911227075100672 |
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| author | Suárez, Fredy Maglorio Sobrado Mendes, Filomena Barbosa Rodrigues |
| author_facet | Suárez, Fredy Maglorio Sobrado Mendes, Filomena Barbosa Rodrigues |
| contents | The emphasis in this paper is on the Coupled System of a Kirchhoff-Love Plate Equation with the Equation of a Membrane-like Electrical Network, where the coupling is of higher order given by the Laplacian of the displacement velocity $γΔu_t$ and the Laplacian of the potential electric field $γΔv_t $, here only one of the equations is conservative, and the other has dissipative properties. The mechanism was dissipative is given by an intermediate damping $(-Δ)^θv_t$ between the potential electric $θ=0$ (frictional damping) and the Laplacian of the electric potential for $θ=1$ (damping Kelvin Voigt). We show that $S(t)=e^{\mathbb{B}t}$ is not analytic for $θ\in [0, 1[$ and analytic for $θ=1$, however $S(t)=e^{\mathbb{B}t}$ decays exponentially for $0\leq θ\leq 1$ and $S(t)$ is of Gevrey sharp class $s>\frac{1}θ$ when the parameter $θ$ lies in the interval $]0,1[$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1908_04826 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | A Gevrey class semigroup, exponential decay and Lack of analyticity for a system formed by a Kirchhoff-Love plate equation and the equation of a membrane-like electric network with indirect fractional damping Suárez, Fredy Maglorio Sobrado Mendes, Filomena Barbosa Rodrigues Analysis of PDEs 35L55 The emphasis in this paper is on the Coupled System of a Kirchhoff-Love Plate Equation with the Equation of a Membrane-like Electrical Network, where the coupling is of higher order given by the Laplacian of the displacement velocity $γΔu_t$ and the Laplacian of the potential electric field $γΔv_t $, here only one of the equations is conservative, and the other has dissipative properties. The mechanism was dissipative is given by an intermediate damping $(-Δ)^θv_t$ between the potential electric $θ=0$ (frictional damping) and the Laplacian of the electric potential for $θ=1$ (damping Kelvin Voigt). We show that $S(t)=e^{\mathbb{B}t}$ is not analytic for $θ\in [0, 1[$ and analytic for $θ=1$, however $S(t)=e^{\mathbb{B}t}$ decays exponentially for $0\leq θ\leq 1$ and $S(t)$ is of Gevrey sharp class $s>\frac{1}θ$ when the parameter $θ$ lies in the interval $]0,1[$. |
| title | A Gevrey class semigroup, exponential decay and Lack of analyticity for a system formed by a Kirchhoff-Love plate equation and the equation of a membrane-like electric network with indirect fractional damping |
| topic | Analysis of PDEs 35L55 |
| url | https://arxiv.org/abs/1908.04826 |