Non-exponential and Polynomial Decay for a Shear Beam With a Gurtin–Pipkin Thermal Law Effective on the Bending Moment

In this work, we study the well-posedness and the asymptotic behavior of a thermoelastic shear beam model, where the heat conduction is given by the Gurtin–Pipkin law acting on the bending moment under Dirichlet–Neumann–Dirichlet boundary conditions. To establish the existence and uniqueness of the solution, we use the semigroup method. Then, we show that the system is not exponentially stable. Ultimately, we prove that the system is polynomially stable.