Non existence de solutions globales de certaines équations d'ondes non linéairesNonexistence of global solutions to some nonlinear wave equations

We study the semilinear wave equation u_tt?Δu=p^?k|u|^m in $\text{R}\text{×}\text{R}{}^{\mathrm{n}}$, where p is a conformal factor approaching 0 at infinity. We prove that the solutions blow-up in finite time for small powers m, while having an arbitrarily long life-span for large m. Furthermore, we study the finite time blow-up of solutions for the class of quasilinear wave equations u_tt?Δu=p^?k|Lu|^m in $\text{R}\text{×}\text{R}{}^{\mathrm{n}}$. To cite this article: M. Aassila, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 961–966.     

RETRACTED: The influence of nonlocal nonlinearities on the long time behavior of solutions of diffusion problems

This article has been retracted at the request of the editor.Reason: This paper was discovered after publication to have been plagiarized from earlier work by Michael Chipot and Luc Molinet, presented in their paper Asymptotic behaviour of some nonlinear diffusion problems, published in volume 80 of Applicable Analysis in 2001 and in the book Elements of Nonlinear Analysis published by Birkhaeuser in 2000. We very much regret this error, and offer our apologies to Professors Chipot and Molinet.     

Stability of Dynamic Models of Suspension Bridges

We study the global existence and asymptotic stability of solutions of dynamic PDE models of suspension bridges.     

Global existence and energy decay for a damped quasi-linear wave equation

In this paper we prove the global existence and study decay property of the solutions to the initial boundary value problem for the quasi-linear wave equation with a dissipative term without the smallness of the initial data. © 1998 B. G. Teubner Stuttgart—John Wiley & Sons, Ltd.     

Existence and uniform decay of the wave equation with nonlinear boundary damping and boundary memory source term

We consider the nonlinear model of the wave equation subject to the following nonlinear boundary conditions We show existence of solutions by means of Faedo-Galerkin method and the uniform decay is obtained by using the multiplier technique. Received: 15 June 2000 / Accepted: 4 December 2000 / Published online: 29 April 2002     

Stabilization of the Korteweg-de Vries-Burgers equation with non-periodic boundary feedbacks

We consider the Korteweg-de Vries-Burgers (KdVB) equation on the domain [0,1]. We derive a control law which guaranteesL ²-global exponential stability,H ³-global asymptotic stability, andH ³-semiglobal exponential stability.     

Some blow-up results for a generalized Ginzburg-Landau equation

We investigate the blow-up of the solution to a complex Ginzburg-Landau like equation in u coupled with a Poisson equation in f\phi defined on the whole space \Bbb Rⁿ, n = 1{\Bbb R}^n, n = 1 or 2.