Asymptotics for nonlinear damped wave equations with large initial data.
Asymptotics of a Time-Splitting Scheme for the Random Schrödinger Equation with Long-Range Correlations
This work is concerned with the asymptotic analysis of a time-splitting scheme for the Schrödinger equation with a random potential having weak amplitude, fast oscillations in time and space, and long-range correlations. Such a problem arises for instance in the simulation of waves propagating in random media in the paraxial approximation. The high-frequency limit of the Schrödinger equation leads to different regimes depending on the distance of propagation, the oscillation pattern of the initial...
Asymptotics of solutions to Stokes and Navier-Stokes equations in domains with paraboloidal outlets to infinity
Asymptotics of the energy functional for a fourth-order mixed boundary value problem in a domain with a cut.
Asymptotics of time harmonic solutions to a thin ferroelectric model.
Asymptotique de Born-Oppenheimer pour la prédissociation moléculaire (cas de potentiels réguliers)
Asymptotique de la phase de diffusion à haute énergie pour l'opérateur de Dirac
Asymptotique de la phase de diffusion à haute énergie pour l'opérateur de Dirac
Asymptotiques de Lifshitz
Cet exposé a pour but de présenter des résultats récents de l’auteur concernant les asymptotiques de Lifshitz pour des perturbations aléatoires d’opérateurs de Schrödinger périodiques. Certains de ces résultats ont été obtenus en collaboration avec T. Wolff.
Asypmtotic Behaviour in Lr for Weak Solutions of the Navier-Stokes Equations in Exterior Domains.
Attractor for a Navier-Stokes flow in an unbounded domain
Attractor for a viscous coupled Camassa-Holm equation.
Attractors of a Schrödinger-Poisson system
Attractors of Strongly Dissipative Systems
A class of infinite-dimensional dissipative dynamical systems is defined for which there exists a unique equilibrium point, and the rate of convergence to this point of the trajectories of a dynamical system from the above class is exponential. All the trajectories of the system converge to this point as t → +∞, no matter what the initial conditions are. This class consists of strongly dissipative systems. An example of such systems is provided by passive systems in network theory (see, e.g., MR0601947...
Auto-Bäcklund transformation and exact analytical solutions for the Kupershmidt equation.
Autour du problème des vortex patches
Auxiliary linear problem, difference Fay identities and dispersionless limit of Pfaff-Toda hierarchy.
Axisymmetric flow of Navier-Stokes fluid in the whole space with non-zero angular velocity component
We study axisymmetric solutions to the Navier-Stokes equations in the whole three-dimensional space. We find conditions on the radial and angular components of the velocity field which are sufficient for proving the regularity of weak solutions.
Backlund Transformations for a Class of Systems of Differential Equation.
Bäcklund transformations for several cases of a type of generalized KdV equation.