Zeitschrift für angewandte Mathematik und Physik

In this paper, we are considering the one-dimensional porous-elastic system with nonlinear localized damping acting in a arbitrary small region of the interval under consideration. Assuming appropriate assumptions on the nonlinear terms, we establish the energy decay of the corresponding system. To do this, we used the observability inequality obtained for the conservative system combined with a unique continuation property recently introduced in Ma et al. (Attractors for locally damped Bresse systems and a unique continuation property, 2021. arXiv:2102.12025 ) and the reduction principle (see Daloutli et al. in Discrete Contin Dyn Syst 2(1):67–94, 2009) where the problem of decay rates with nonlinear damping is reduced to an appropriate stabilizability inequality for the linear equation. This study generalizes and improves previous literature outcomes.

Based on Tresca's yield condition and the associated flow rule, the stress distribution in a rotating solid cylinder of elastic-perfectly plastic material under plane strain is discussed. It is shown that the plastic core consists of two parts with different regimes of the yield condition. With increasing angular velocity, a second plastic zone forms at the boundary and spreads inwards.

Wall interference on an airfoil model in a wind tunnel has been treated as a singular perturbation problem for both subsonic and transonic flows. This problem is formulated within the framework of small perturbation theory. It is shown that the classical interference solution consists of the outer boundary condition for the inner boundary value problem.

In this article, we use the Euler–Bernoulli model to study the vibrations of a beam composed of two components, one consisting of a thermoelastic material and the other of a simply elastic material that does not produce dissipation. Our main result is that the semigroup associated with this model is differentiable. In particular, our proof implies the following properties of the semigroup (1) It is of Gevrey class 12. (2) It is exponentially stable. (3) It possesses the property of linear stability and has a regularizing effect on the initial data.