Convolution Semigroups and Generalized Telegraph Equations.
Cordes vibrantes non linéaires
Couches limites pour des problèmes mixtes hyperboliques
Couches limites semilinéaires
On s’intéresse à des problèmes mixtes pour des systèmes symétriques hyperboliques multidimensionnels semilinéaires perturbés par une petite viscosité. La description à la limite non visqueuse recquiert des développements du type BKW mettant en évidence une couche limite caractéristique (CLC) et une couche limite non caractéristique (CLNC). Ce thème traité dans [12] est ici enrichi de trois améliorations :l’étude inclut des développements ayant peu de termes (comme un seul terme),on étudie aussi...
Counterexamples to local existence for nonlinear wave equations
Counterexamples to the Strichartz inequalities for the wave equation in general domains with boundary
In this paper we consider a smooth and bounded domain of dimension with boundary and we construct sequences of solutions to the wave equation with Dirichlet boundary condition which contradict the Strichartz estimates of the free space, providing losses of derivatives at least for a subset of the usual range of indices. This is due to microlocal phenomena such as caustics generated in arbitrarily small time near the boundary. Moreover, the result holds for microlocally strictly convex domains...
Critical phenomena in gravitational collapse
A mini-introduction to critical phenomena in gravitational collapse is combined with a more detailed discussion of how gravity regularizes the 'critical spacetimes' that dominate these phenomena.
Croissance asymptotique des solutions de l'équation des ondes sur une variété riemannienne compacte à courbure négative
Cubic Quasilinear wave equation and bilinear estimates
Darboux and Goursat type problems in the trihedral angle for hyperbolic type equations of third order
Das Rand-Anfangswertproblem für quasilineare Wellengleichungen in Sobolevräumen niedriger Ordnung.
Das Verhalten der Ableitungen globaler Lösungen nicht-linearer Wellengleichungen für grosse Zeiten.
Das Verhalten globaler Lösungen nichtlinearer Wellengleichungen für große Zeiten.
Decacy of solutions of the wave equation with a local nonlinear dissipation.
Decay estimates for spherically symmetric Yang-Mills fields in Minkowski space-time
Decay estimates for the critical semilinear wave equation
Decay estimates of solutions of a nonlinearly damped semilinear wave equation
We consider an initial boundary value problem for the equation . We first prove local and global existence results under suitable conditions on f and g. Then we show that weak solutions decay either algebraically or exponentially depending on the rate of growth of g. This result improves and includes earlier decay results established by the authors.
Decay of positive waves in nonlinear systems of conservation laws
Decay of solutions of a degenerate hyperbolic equation.
Decay of solutions of a nonlinear hyperbolic system in noncylindrical domain.