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- Saïd Benachour, Simona Dabuleanu-Hapca, Philippe Laurençot
- Asymptotic Analysis
- 2007

Global classical solutions to the viscous Hamilton-Jacobi equation ut − ∆u = a |∇u| p in (0, ∞) × Ω with homogeneous Dirichlet boundary conditions are shown to converge to zero in W 1,∞ (Ω) at the same speed as the linear heat semigroup when p > 1. For p = 1, an exponential decay to zero is also obtained in one space dimension but the rate depends on a and… (More)

- BELGACEM REBIAI, SAÏD BENACHOUR
- 2010

The aim of this study is to construct the invariant regions in which we can establish the global existence of classical solutions for reaction-diffusion systems with a general full matrix of diffusion coefficients. Our techniques are based on invariant regions and Lyapunov functional methods. The nonlinear reaction term has been supposed to be of… (More)

- BELGACEM REBIAI, SAÏD BENACHOUR
- 2009

The aim of this study is to prove global existence of classical solutions for problems of the form ∂u ∂t − a∆u = −f (u, v), ∂v ∂t − b∆v = g(u, v) in (0, +∞) × Ω where Ω is an open bounded domain of class C 1 in R n , a > 0, b > 0, a = b and f , g are nonnegative continuously differentiable functions on [0, +∞) × [0, +∞) satisfying f (0, η) = 0, g(ξ, η) ≤… (More)

- SAÏD BENACHOUR
- 2008

Sharp temporal decay estimates are established for the gradient and time derivative of solutions to the Hamilton-Jacobi equation ∂tvε + H(|∇xvε|) = ε ∆vε in R N × (0, ∞), the parameter ε being either positive or zero. Special care is given to the dependence of the estimates on ε. As a by-product, we obtain convergence of the sequence (vε) as ε → 0 to a… (More)

- S. Benachour
- 2013

In this paper we consider the problem of global asymptotic stabilization with prescribed local behavior. We show that this problem can 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 has the value function of an… (More)

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