Muhammad I. Mustafa

Plate equations with frictional and viscoelastic dampings

In this paper, we consider the plate equation with both weak frictional damping and viscoelastic damping acting simultaneously and complementarily in the domain. An energy decay rate formula is obtained under nonrestrictive hypotheses on the relaxation function and the frictional damping term. Our results improve and generalize previous results existing in the literature.

Energy Decay in a Quasilinear System with Finite and Infinite Memories

In this paper, we consider the following quasilinear system of two coupled nonlinear equations with both finite and infinite memories

Exponential Decay in Thermoelastic Systems with Internal Distributed Delay

\displaystyle \left \{ \begin {array}{l} \left \vert u_{t}\right \vert ^{\rho }u_{tt}-\Delta u-\Delta u_{tt}+\int _{0}^{t}g_{1}(s)\Delta u(t-s)ds+f_{1}(u,v)=0 \\ \left \vert v_{t}\right \vert ^{\rho }v_{tt}-\Delta v-\Delta v_{tt}+\int _{0}^{\infty }g_{2}(s)\Delta v(t-s)ds+f_{2}(u,v)=0 \end {array} \right .

Decay rates for memory‐type plate system with delay and source term

and investigate the asymptotic behavior of this system. We use the multiplier method to establish an explicit energy decay formula. Our result allows a wider class of relaxation functions and provides more general decay rates for which the usual exponential and polynomial rates are only special cases. AMS Classification35B40, 74D99, 93D15, 93D20

Energy decay for viscoelastic plates with distributed delay and source term

In this paper, we consider a laminated beam model. This structure is given by two identical uniform layers on top of each other, taking into account that an adhesive of small thickness is bonding the two surfaces and produces an interfacial slip. We use boundary feedback control and establish an exponential energy decay result. Our result improves the earlier related results in the literature.In this paper, we consider a laminated beam model. This structure is given by two identical uniform layers on top of each other, taking into account that an adhesive of small thickness is bonding the two surfaces and produces an interfacial slip. We use boundary feedback control and establish an exponential energy decay result. Our result improves the earlier related results in the literature.