The Riemann problem for -systems with continuous flux function
The Riemann problem in gasdynamics.
The role of the Lagrange constant in some nonlinear waves equations.
The ROTHE method for nonlinear hyperbolic problems
The Runge-Kutta local projection -discontinuous-Galerkin finite element method for scalar conservation laws
The second-order Klein-Gordon field equation.
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,...