On the weakly nonlinear wave equation involving a small parameter at the highest derivative
On the well posedness of a system of balance laws with data
On the well-balance property of Roe’s method for nonconservative hyperbolic systems. Applications to shallow-water systems
This paper is concerned with the numerical approximations of Cauchy problems for one-dimensional nonconservative hyperbolic systems. The first goal is to introduce a general concept of well-balancing for numerical schemes solving this kind of systems. Once this concept stated, we investigate the well-balance properties of numerical schemes based on the generalized Roe linearizations introduced by [Toumi, J. Comp. Phys. 102 (1992) 360–373]. Next, this general theory is applied to obtain well-balanced...
On the well-balance property of Roe's method for nonconservative hyperbolic systems. applications to shallow-water systems
This paper is concerned with the numerical approximations of Cauchy problems for one-dimensional nonconservative hyperbolic systems. The first goal is to introduce a general concept of well-balancing for numerical schemes solving this kind of systems. Once this concept stated, we investigate the well-balance properties of numerical schemes based on the generalized Roe linearizations introduced by [Toumi, J. Comp. Phys.102 (1992) 360–373]. Next, this general theory is applied to obtain well-balanced...
On the well-posedness and regularity of the wave equation with variable coefficients
An open-loop system of a multidimensional wave equation with variable coefficients, partial boundary Dirichlet control and collocated observation is considered. It is shown that the system is well-posed in the sense of D. Salamon and regular in the sense of G. Weiss. The Riemannian geometry method is used in the proof of regularity and the feedthrough operator is explicitly computed.
On the wellposedness in the Gevrey classes of the Cauchy problem for weakly hyperbolic equations whose coefficients are Hölder continuous in and degenerate in
On time optimal control of the wave equation, its regularization and optimality system
An approximation procedure for time optimal control problems for the linear wave equation is analyzed. Its asymptotic behavior is investigated and an optimality system including the maximum principle and the transversality conditions for the regularized and unregularized problems are derived.
On unique solvability of the periodic problem in the plane for linear hyperbolic equations.
On uniqueness and existence of entropy solutions of weakly coupled systems of nonlinear degenerate parabolic equations.
On volumetric growth and material frames.
On weak solution to a hyperbolic differential inclusion with nonmonotone discontinuous nonlinear term.
On weak solutions of semilinear hyperbolic-parabolic equations.
Ondes de raréfaction pour des systèmes quasilinéaires hyperboliques multidimensionnels
Ondes hyperboliques non linéaires globales
Ondes lentes et interaction contrôlée pour les équations strictement hyperboliques non linéaires
Ondes oscillantes semi-linéaires en 1.d
Ondes oscillantes simples quasilinéaires
Ondes soniques
One-dimensional adhesion model for large scale structures.
Opérateurs hyperboliques à caractéristiques de multiplicité constante
Soit un opérateur hyperbolique à caractéristiques de multiplicité constante. On sait que le problème de Cauchy est mal posé si on n’impose pas une condition, dite de Lévi, sur les termes d’ordre inférieur. On démontre que cette condition implique la possibilité de construire une paramétrix du problème de Cauchy au moyen des opérateurs intégraux de Fourier. On en déduit la résolubilité du problème de Cauchy dans les fonctions et dans les espaces de Sobolev.