Paramétrix d’opérateurs elliptiques de classe
Paramétrix pour un problème de Cauchy hyperbolique à multiplicité variable
Partial integral operators in Orlicz spaces with mixed norm
Pattern and Waves for a Model in Population Dynamics with Nonlocal Consumption of Resources
We study a reaction-diffusion equation with an integral term describing nonlocal consumption of resources in population dynamics. We show that a homogeneous equilibrium can lose its stability resulting in appearance of stationary spatial structures. They can be related to the emergence of biological species due to the intra-specific competition and random mutations. Various types of travelling waves are observed.
Periodic solutions of some linear systems of differential equations.
Polynomials in the Volterra and Ritt operators
We continue the paper [Ts] on the boundedness of polynomials in the Volterra operator. This provides new ways of constructing power-bounded operators. It seems interesting to point out that a similar procedure applies to the operators satisfying the Ritt resolvent condition: compare Theorem 5 and Theorem 9 below.
Potential operators in variable exponent Lebesgue spaces: two-weight estimates.
Potential type operators on curves with vorticity points.
Principal matrix solutions and variation of parameters for a Volterra integro-differential equation and its adjoint.
Problèmes de Cauchy hyperboliques en dimension infinie
Problemi inversi, equazioni quasilineari e semigruppi analitici
Propagation des singularités différentiables pour des opérateurs différentiels à coefficients analytiques
Propagation of singularities and maximal functions in the plane.
Propagation of Singularities for Non Real Pseudo-Differential Operators
Properties of eigenfunctions of non-local operators
Pseudodifferential analysis on continuous family groupoids.
Pseudodifferential Operators
Pseudo-Differential Operators in a Wave Diffraction Problem with Impedance Conditions
Mathematics Subject Classification: 35J05, 35J25, 35C15, 47H50, 47G30We consider an impedance boundary-value problem for the Helmholtz equation which models a wave diffraction problem with imperfect conductivity on a strip. Pseudo-differential operators are used to deal with this wave diffraction problem. Therefore, single and double layer potentials allow a reformulation of the problem into a system of integral equations. By using operator theoretical methods, the well-posedness of the problem...
Pseudodifferential operators on non-quasianalytic classes of Beurling type
We introduce pseudodifferential operators (of infinite order) in the framework of non-quasianalytic classes of Beurling type. We prove that such an operator with (distributional) kernel in a given Beurling class is pseudo-local and can be locally decomposed, modulo a smoothing operator, as the composition of a pseudodifferential operator of finite order and an ultradifferential operator with constant coefficients in the sense of Komatsu, both operators with kernel in the same class . We also...
Pseudo-spectrum for a class of semi-classical operators
We study in this paper a notion of pseudo-spectrum in the semi-classical setting called injectivity pseudo-spectrum. The injectivity pseudo-spectrum is a subset of points in the complex plane where there exist some quasi-modes with a precise rate of decay. For that reason, these values can be considered as some ‘almost eigenvalues’ in the semi-classical limit. We are interested here in studying the absence of injectivity pseudo-spectrum, which is characterized by a global a priori estimate. We prove...