Gradient estimates for a degenerate parabolic equation with gradient absorption and applications

Qualitative properties of non-negative solutions to a quasilinear degenerate parabolic equation with an absorption term depending solely on the gradient are shown, providing information on the competition between the nonlinear diffusion and the nonlinear absorption. In particular, the limit as time goes to infinity of the mass of integrable solutions is identified, together with the rate of expansion of the support for compactly supported initial data. The persistence of dead cores is also shown. The proof of these results strongly relies on gradient estimates which are first established

Large time behavior for a viscous Hamilton-Jacobi equation with Neumann boudary condition

We prove the existence and the uniqueness of strong solutions for the viscous Hamilton-Jacobi Equation with Neumann boundary condition and initial data a continious function. Then, we study the large time behavior of the solutions.Comment: 32 page

Sharp Decay Estimates and Vanishing Viscosity for Diffusive Hamilton-Jacobi Equations

Sharp temporal decay estimates are established for the gradient and time derivative of solutions to a viscous Hamilton-Jacobi equation as well the associated Hamilton-Jacobi equation. Special care is given to the dependence of the estimates on the viscosity. The initial condition being only continuous and either bounded or non-negative. The main requirement on the Hamiltonians is that it grows superlinearly or sublinearly at infinity, including in particular H(r) = r^p for r non-negatif and p positif and different from 1.Comment: 20 page

Locally optimal controllers and globally inverse optimal controllers

In this paper we consider the problem of global asymptotic stabilization with prescribed local behavior. We show that this problem can be formulated in terms of control Lyapunov functions. Moreover, we show that if the local control law has been synthesized employing a LQ approach, then the associated Lyapunov function can be seen as the value function of an optimal problem with some specific local properties. We illustrate these results on two specific classes of systems: backstepping and feedforward systems. Finally, we show how this framework can be employed when considering the orbital transfer problem

Prediction of Fatigue Crack Growth of Repaired Al-alloy Structures with Double Sides

AbstractDuring navigation, aircrafts are subject to fatigue damage. In order to rehabilitate damaged structures some techniques are often used to resolve this problem. Efficient repair technique, called composite patch repair, was used to reinforce the damaged structures and stop cracks. In this paper, effect of composite patch repair (Boron/Epoxy) on fatigue crack growth (FCG) was investigated on 2219 T62 Al-alloy. Effects of double patch repair in single notch tensile specimen (SENT) on FCG were studied and compared to single patch repair. Results show beneficial effect of patch repair on fatigue life and FCGR in comparison with the un-patched specimen. In addition, effect of mean stress characterized by stress ratio was highlighted. Fatigue behavior of investigated Al-alloy was compared

Effect of Single Overload Ratio and Stress Ratio on Fatigue Crack Growth

In this investigation, variation of cyclic loading effect on fatigue crack growth is studied. This study is performed on 2024 T351 and 7050-T74 aluminum alloys, used in aeronautical structures. The propagation model used in this study is NASGRO model. In constant amplitude loading (CA), the effect of stress ratio has been investigated. Fatigue life and fatigue crack growth rate were affected by this factor. Results showed an increasing in fatigue crack growth rates (FCGRs) with increasing stress ratio. Variable amplitude loading (VAL) can take many forms i.e with a single overload, overload band etc. The shape of these loads affects strongly the fracture life and FCGRs. The application of a single overload (ORL) decrease the FCGR and increase the delay crack length caused by the formation of a larger plastic zone compared to the plastic zone due without VAL. The fatigue behavior of the both material under single overload has been compared