Long time behavior and numerical treatment of shear beam model subject to a delay
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In this paper, we consider a one-dimensional system known as Shear beam model (no rotary inertia) where the transverse displacement equation is subject to a delay. Under suitable assumptions on the weight of the delay, we first achieved the global well-posedness of the system by using the classical Faedo-Galerkin approximations along with three a priori estimates. Next, we study the asymptotic behavior of solution using the energy method. Later we propose a discretization based on P1-finite element for space and implicit Euler scheme for time, where a discrete stability property and a priori error estimates of the discrete problem are proved. Finally, some numerical simulations are presented.
Abstract
In this paper, we consider a one-dimensional system known as Shear beam model (no rotary inertia) where the transverse displacement equation is subject to a delay. Under suitable assumptions on the weight of the delay, we first achieved the global well-posedness of the system by using the classical Faedo-Galerkin approximations along with three a priori estimates. Next, we study the asymptotic behavior of solution using the energy method. Later we propose a discretization based on P1-finite element for space and implicit Euler scheme for time, where a discrete stability property and a priori error estimates of the discrete problem are proved. Finally, some numerical simulations are presented.