Saïd Benachour

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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 (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)
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)
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 in R, a > 0, b > 0, a 6= b and f , g are nonnegative continuously differentiable functions on [0,+∞)× [0,+∞) satisfying f(0, η) = 0, g(ξ, η) ≤ Cφ(ξ)e β and(More)
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 × (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)
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