On the profiles of nonlinear geometric optics
On the radius of spatial analyticity for the higher order nonlinear dispersive equation
In this work, using bilinear estimates in Bourgain type spaces, we prove the local existence of a solution to a higher order nonlinear dispersive equation on the line for analytic initial data . The analytic initial data can be extended as holomorphic functions in a strip around the -axis. By Gevrey approximate conservation law, we prove the existence of the global solutions, which improve earlier results of Z. Zhang, Z. Liu, M. Sun, S. Li, (2019).
On the relation between the Borel sum and the classical solution of the Cauchy problem for certain partial differential equations
On the representation of non-negative solutions of linear parabolic systems of partial differential equations
On the singular behavior of solutions of a transmission problem in a dihedral.
On the singular limit of solutions to the Cox-Ingersoll-Ross interest rate model with stochastic volatility
In this paper we are interested in term structure models for pricing zero coupon bonds under rapidly oscillating stochastic volatility. We analyze solutions to the generalized Cox–Ingersoll–Ross two factors model describing clustering of interest rate volatilities. The main goal is to derive an asymptotic expansion of the bond price with respect to a singular parameter representing the fast scale for the stochastic volatility process. We derive the second order asymptotic expansion of a solution...
On the Singularities of the Solution to the Cauchy Problem with Singular Data in the Complex Domain.
On the solution of boundary value problems for linear parabolic equations of higher order
On the solutions of Knizhnik-Zamolodchikov system
We consider the Knizhnik-Zamolodchikov system of linear differential equations. The coefficients of this system are rational functions. We prove that under some conditions the solution of the KZ system is rational too. We give the method of constructing the corresponding rational solution. We deduce the asymptotic formulas for the solution of the KZ system when the parameter ρ is an integer.
On the speed of spread for fractional reaction-diffusion equations.
On the Theory of Exterior Elastic Herglotz Functions
On transformations of the Rabelo equations.
Ondes oscillantes simples quasilinéaires
Ondes semi-linéaires conormales classiques par rapport à deux hypersurfaces transverses
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...
Optimal energy decay rate of coupled wave equations.
Optimal Lipschitz estimates for the equation on a class of convex domains
Optique Géométrique et invariance de jauge : Solutions oscillantes d’amplitude critique pour les équations de Yang-Mills