A blow up condition for a nonautonomous semilinear system.
A decay estimate for a class of hyperbolic pseudo-differential equations
We consider the equation , where is a first order pseudo-differential operator with real symbol . Under a suitable convexity assumption on we find the decay properties for . These can be applied to the linear Maxwell system in anisotropic media and to the nonlinear Cauchy Problem , . If is a smooth function which satisfies near , and is small in suitably Sobolev norm, we prove global existence theorems provided is greater than a critical exponent.
A Fractional Analog of the Duhamel Principle
Mathematics Subject Classification: 35CXX, 26A33, 35S10The well known Duhamel principle allows to reduce the Cauchy problem for linear inhomogeneous partial differential equations to the Cauchy problem for corresponding homogeneous equations. In the paper one of the possible generalizations of the classical Duhamel principle to the time-fractional pseudo-differential equations is established.* This work partially supported by NIH grant P20 GMO67594.
An analysis of quantum Fokker-Planck models: a Wigner function approach.
The analysis of dissipative transport equations within the framework of open quantum systems with Fokker-Planck-type scattering is carried out from the perspective of a Wigner function approach. In particular, the well-posedness of the self-consistent whole-space problem in 3D is analyzed: existence of solutions, uniqueness and asymptotic behavior in time, where we adopt the viewpoint of mild solutions in this paper. Also, the admissibility of a density matrix formulation in Lindblad form with Fokker-Planck...
Analyse microlocale et équations d’évolution
Application de la théorie des microfonctions holomorphes au problème de Cauchy à données singulières
Asymptotics for critical nonconvective type equations.
Existence by minimisation of solitary water waves on an ocean of infinite depth
Fourier integral operators of infinite order on with an application to a certain Cauchy problem
Gradient flows of the entropy for jump processes
We introduce a new transport distance between probability measures on that is built from a Lévy jump kernel. It is defined via a non-local variant of the Benamou–Brenier formula. We study geometric and topological properties of this distance, in particular we prove existence of geodesics. For translation invariant jump kernels we identify the semigroup generated by the associated non-local operator as the gradient flow of the relative entropy w.r.t. the new distance and show that the entropy is...
Initial Value Problems in Lp for Systems with Variable Coefficients.
Intégrales premières analytiques des équations différentielles paraboliques non linéaires et du système des équations de Navier-Stokes. Applications à la théorie des solutions statistiques et à d'autres problèmes
Le problème de Cauchy à caractéristiques multiples
Le problème de Cauchy à caractéristiques multiples - II
Le problème de Goursat non-linéaire
Le théorème de Nishida pour le problème de Cauchy abstrait par une méthode de point fixe
Les moments microlocaux et la régularité des solutions de l'équation de Schrödinger
Local and global nonexistence of solutions to semilinear evolution equations.
Necessary conditions for local and global existence to a reaction-diffusion system with fractional derivatives.
Nonlinear pseudodifferential equations on a half-line with large initial data.