On a generalized nonlinear equation of Schrödinger type.
On a parabolic-hyperbolic Penrose-Fife phase-field system.
On a theorem of Cauchy-Kovalevskaya type for a class of nonlinear PDE's of higher order with deviating arguments
We prove an existence theorem of Cauchy-Kovalevskaya type for the equation where f is a polynomial with respect to the last k variables.
On a time-dependent subdifferential evolution inclusion with a nonconvex upper-semicontinuous perturbation.
On analytic solutions to the generalized Cauchy problem with data on three surfaces for a quasilinear system.
On existence and nonexistence results for nonlinear Schrödinger equations
On Solutions of the Initial Value Problem for the Nonlinear Schrödinger Equations in One Space Dimension.
On the global Cauchy problem for some non linear Schrödinger equations
On the support of solutions to the generalized KdV equation
On the Uniqueness of Solutions and on the Convergence of Successive Approximations for Certain Initial Problems of Equations of the Higher Orders
On uniqueness and stability of steady-state carrier distributions in semiconductors
Opérateurs de Fuchs non linéaires
On se propose d’étudier des équations aux dérivées partielles non linéaires du type de Fuchs au sens de Baouendi-Goulaouic ([1] et [2]) dans des espaces de fonctions suffisamment différentiables par rapport à la variable fuchsienne et dans des espaces de Gevrey par rapport aux autres variables. Les méthodes utilisées reposent sur le formalisme des séries formelles Gevrey développé dans [13] et adapté aux équations du type de Fuchs dans [6] et [7]. On obtient ainsi des théorèmes qui généralisent...
Porous medium equation and fast diffusion equation as gradient systems
We show that the Porous Medium Equation and the Fast Diffusion Equation, , with , can be modeled as a gradient system in the Hilbert space , and we obtain existence and uniqueness of solutions in this framework. We deal with bounded and certain unbounded open sets and do not require any boundary regularity. Moreover, the approach is used to discuss the asymptotic behaviour and order preservation of solutions.
Positive periodic solutions for the Korteweg-de Vries equation.
Problème de Cauchy global pour des systèmes de Dirac-Klein-Gordon
Problème de Cauchy pour des systèmes hyperboliques semi-linéaires
Propagation of uniform Gevrey regularity of solutions to evolution equations
We investigate the propagation of the uniform spatial Gevrey , σ ≥ 1, regularity for t → +∞ of solutions to evolution equations like generalizations of the Euler equation and the semilinear Schrödinger equation with polynomial nonlinearities. The proofs are based on direct iterative arguments and nonlinear Gevrey estimates.
Remarque sur le problème de Cauchy pour une équation de Dirac non linéaire avec masse nulle
Residual models for nonlinear partial differential equations.
Solution of singular and nonsingular initial and boundary value problems by modified variational iteration method.