The Semilinear Second-Order Hyperbolic Equation with Data Strongly Singular at One Point.
The shallow water equations: Conservation laws and symplectic geometry.
The sharp-interface approach for fluids with phase change: Riemann problems and ghost fluid techniques
Systems of mixed hyperbolic-elliptic conservation laws can serve as models for the evolution of a liquid-vapor fluid with possible sharp dynamical phase changes. We focus on the equations of ideal hydrodynamics in the isothermal case and introduce a thermodynamically consistent solution of the Riemann problem in one space dimension. This result is the basis for an algorithm of ghost fluid type to solve the sharp-interface model numerically. In particular the approach allows to resolve phase transitions...
The simplified Wheeler-Dewitt equation : the Cauchy problem and some spectral properties
The Sinc Method in Multiple Space Dimensions: Model Probelms.
The symbol of a lagrangian distribution
The third boundary value problem for a nonlinear system of second order hyperbolic integro-differential equations
The two-dimensional eikonal equation.
The uniform exponential stability and the uniform stability at constantly acting disturbances of a periodic solution of a wave equation
The wave equation with oscillating density : observability at low frequency
The wave equation with oscillating density : observability at low frequency
The wave equation with oscillating density: observability at low frequency
We prove an observability estimate for a wave equation with rapidly oscillating density, in a bounded domain with Dirichlet boundary condition.
The Wave Group and Radiation Fields on Asymptotically Hyperbolic Manifolds
The wave map problem. Small data critical regularity
The paper provides a description of the wave map problem with a specific focus on the breakthrough work of T. Tao which showed that a wave map, a dynamic lorentzian analog of a harmonic map, from Minkowski space into a sphere with smooth initial data and a small critical Sobolev norm exists globally in time and remains smooth. When the dimension of the base Minkowski space is , the critical norm coincides with energy, the only manifestly conserved quantity in this (lagrangian) theory. As a consequence,...
The well-posedness of the Dirichlet problem in the cylindric domain for the multidimensional wave equation.
Théorie de la diffusion pour l'équation de sinus-Gordon à trois dimensions
Théorie spectrale de la propagation des ondes acoustiques dans un milieu stratifié perturbe
Theory and numerical approximations for a nonlinear 1 + 1 Dirac system
We consider a nonlinear Dirac system in one space dimension with periodic boundary conditions. First, we discuss questions on the existence and uniqueness of the solution. Then, we propose an implicit-explicit finite difference method for its approximation, proving optimal order a priori error estimates in various discrete norms and showing results from numerical experiments.
Theory and numerical approximations for a nonlinear 1 + 1 Dirac system
We consider a nonlinear Dirac system in one space dimension with periodic boundary conditions. First, we discuss questions on the existence and uniqueness of the solution. Then, we propose an implicit-explicit finite difference method for its approximation, proving optimal order a priori error estimates in various discrete norms and showing results from numerical experiments.
Thick obstacle problems with dynamic adhesive contact
In this work, we consider dynamic frictionless contact with adhesion between a viscoelastic body of the Kelvin-Voigt type and a stationary rigid obstacle, based on the Signorini's contact conditions. Including the adhesion processes modeled by the bonding field, a new version of energy function is defined. We use the energy function to derive a new form of energy balance which is supported by numerical results. Employing the time-discretization, we establish a numerical formulation and investigate...