The blow-up curve of solutions of mixed problems for semilinear wave equations with exponential nonlinearities in one space dimension, II
The Cauchy problem for a nonlinear Wheeler-DeWitt equation
The Cauchy problem for nonlinear wave equations in the homogeneous Sobolev space
The Cauchy problem for semilinear weakly hyperbolic equations in Hilbert spaces
The Cauchy problem for wave equations with non Lipschitz coefficients; Application to continuation of solutions of some nonlinear wave equations
In this paper we study the Cauchy problem for second order strictly hyperbolic operators of the form when the coefficients of the principal part are not Lipschitz continuous, but only “Log-Lipschitz” with respect to all the variables. This class of equation is invariant under changes of variables and therefore suitable for a local analysis. In particular, we show local existence, local uniqueness and finite speed of propagation for the noncharacteristic Cauchy problem. This provides an invariant...
The critical case for a semilinear weakly hyperbolic equation.
The existence of homoclinic solutions for hyperbolic equations.
The FBI transform, operators with nonsmooth coefficients and the nonlinear wave equation
The aim of this work is threefold. First we set up a calculus for partial differential operators with nonsmooth coefficients which is based on the FBI (Fourier-Bros-Iagolnitzer) transform. Then, using this calculus, we prove a weaker version of the Strichartz estimates for second order hyperbolic equations with nonsmooth coefficients. Finally, we apply these new Strichartz estimates to second order nonlinear hyperbolic equations and improve the local theory, i.e. prove local well-posedness for initial...
The Global Cauchy Problem for the Non Linear Klein-Gordon Equation.
The global Cauchy problem for the non linear Klein-Gordon equation-II
The global solubility of problems of nonlinear vibrations of plates on nonlinear foundations.
The initial-boundary value problem for the non-barotropic compressible Euler equations : structural-stability and data dependence
The role of the Lagrange constant in some nonlinear waves equations.
The Semilinear Second-Order Hyperbolic Equation with Data Strongly Singular at One Point.
The third boundary value problem for a nonlinear system of second order hyperbolic integro-differential equations
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,...
Time Decay for Nonlinear Wave Equations in Two Space Dimensions.
Time Periodic Solutions of Nonlinear Wave Equations.
Time-periodic solutions of a quasilinear beam equation via accelerated convergence methods
The author investigates time-periodic solutions of the quasilinear beam equation with the help of accelerated convergence methods. Using the Newton iteration scheme, the problem is approximated by a sequence of linear equations solved via the Galerkin method. The derivatiove loss inherent to this kind of problems is compensated by taking advantage of smoothing operators.
Time-periodic solutions of telegraph equations in spatial variables