Point fixe d'une application non contractante.
We study a multilinear fixed-point equation in a closed ball of a Banach space where the application is 1-Lipschitzian: existence, uniqueness, approximations, regularity.
Pointwise bounds on the asymptotics of spherically averaged -solutions of one-body Schrödinger equations
Poisson relation for the scattering kernel and inverse scattering by obstacles
Poisson-Lie groups and complete integrability. I. Drinfeld bigebras, dual extensions and their canonical representations
Polynomial solutions to the Hele--Shaw problem.
Positive periodic solutions for the Korteweg-de Vries equation.
Positive solutions for nonlinear Schrödinger equations with deepening potential well
Positivity theorem
Potential Scattering in a Homogeneous Electrostatic Field.
Power series solution for the modified KdV equation.
Prediction-correction legendre spectral scheme for incompressible fluid flow
The initial-boundary value problem of two-dimensional incompressible fluid flow in stream function form is considered. A prediction-correction Legendre spectral scheme is proposed, which is easy to be performed. The numerical solution possesses the accuracy of second-order in time and higher order in space. The numerical experiments show the high accuracy of this approach.
Predictive extension of a singular lagrangian system
Prescribing mean curvature: existence and uniqueness problems.
Pressure conditions for the local regularity of solutions of the Navier-Stokes equations.
Preuve de la conjecture de Lieb-Thirring dans le cas des potentiels quadratiques strictement convexes
Probabilistic analysis of singularities for the 3-D Navier-Stokes equations
Probabilistic analysis of singularities for the 3D Navier-Stokes equations
The classical result on singularities for the 3D Navier-Stokes equations says that the -dimensional Hausdorff measure of the set of singular points is zero. For a stochastic version of the equation, new results are proved. For statistically stationary solutions, at any given time , with probability one the set of singular points is empty. The same result is true for a.e. initial condition with respect to a measure related to the stationary solution, and if the noise is sufficiently non degenerate...
Probabilistic interpretation and random walk on spheres algorithms for the Poisson-Boltzmann equation in molecular dynamics
Motivated by the development of efficient Monte Carlo methods for PDE models in molecular dynamics, we establish a new probabilistic interpretation of a family of divergence form operators with discontinuous coefficients at the interface of two open subsets of . This family of operators includes the case of the linearized Poisson-Boltzmann equation used to compute the electrostatic free energy of a molecule. More precisely, we explicitly construct a Markov process whose infinitesimal generator...
Probability & incompressible Navier-Stokes equations: an overview of some recent developments.
Probing methods for saddle-point problems.