Optique Géométrique et invariance de jauge : Solutions oscillantes d’amplitude critique pour les équations de Yang-Mills
Optique non linéaire et ondes sur critiques
Oscillation criteria for nonlinear inhomogeneous hyperbolic equations with distributed deviating arguments.
Oscillation of nonlinear impulsive hyperbolic equations with several delays.
Oscillations of the solutions of nonlinear hyperbolic equations of neutral type.
In this paper nonlinear hyperbolic equations of neutral type of a given form are considered, with certain boundary conditions. Under certain constraints on the coefficients of the equation and the boundary conditions, sufficient conditions for oscillation of the solutions of the problems considered are obtained.
P-adaptive Hermite methods for initial value problems∗
We study order-adaptive implementations of Hermite methods for hyperbolic and singularly perturbed parabolic initial value problems. Exploiting the facts that Hermite methods allow the degree of the local polynomial representation to vary arbitrarily from cell to cell and that, for hyperbolic problems, each cell can be evolved independently over a time-step determined only by the cell size, a relatively straightforward method is proposed. Its utility is demonstrated on a number of model problems...
P-adaptive Hermite methods for initial value problems
We study order-adaptive implementations of Hermite methods for hyperbolic and singularly perturbed parabolic initial value problems. Exploiting the facts that Hermite methods allow the degree of the local polynomial representation to vary arbitrarily from cell to cell and that, for hyperbolic problems, each cell can be evolved independently over a time-step determined only by the cell size, a relatively straightforward method is proposed. Its utility is demonstrated on a number of model problems...
P-adaptive Hermite methods for initial value problems∗
We study order-adaptive implementations of Hermite methods for hyperbolic and singularly perturbed parabolic initial value problems. Exploiting the facts that Hermite methods allow the degree of the local polynomial representation to vary arbitrarily from cell to cell and that, for hyperbolic problems, each cell can be evolved independently over a time-step determined only by the cell size, a relatively straightforward method is proposed. Its utility is demonstrated on a number of model problems...
Paracomposition et application aux équations non-linéaires
Periodic and invariant measures for stochastic wave equations.
Periodic Solutions of a Nonlinear Wave Equation Without Assumption of Monotonicity.
Periodic solutions of nonlinear wave equations with non-monotone forcing terms
Existence and regularity of periodic solutions of nonlinear, completely resonant, forced wave equations is proved for a large class of non-monotone forcing terms. Our approach is based on a variational Lyapunov-Schmidt reduction. The corresponding infinite dimensional bifurcation equation exhibits an intrinsic lack of compactness. This difficulty is overcome finding a-priori estimates for the constrained minimizers of the reduced action functional, through techniques inspired by regularity theory...
Periodic solutions of partial differential equations with hysteresis
Periodic solutions of weakly nonlinear wave equations in unbounded intervals
Periodic solutions to a one-dimensional strongly nonlinear wave equation with strong dissipation
Periodic solutions to the inhomogeneous sine-Gordon equation
Perte de régularité pour les équations d’ondes sur-critiques
On prouve que le problème de Cauchy local pour l’équation d’onde sur-critique dans , , impair, avec et , est mal posé dans pour tout , où est l’exposant critique.
Perturbation of a solitary wave of the nonlinear Klein-Gordon equation.
Perturbations singulières d'équations hyperboliques du second ordre non linéaires
Perturbations singulières pour une équation hyperbolique dégénérée