Principe d'extremum relatif aux solutions de l'équation intégro-différentielle du processus stochastique markovien mixte
Problème de Cauchy pour l'équation de Boltzmann en relativité générale
Problème de Dirichlet intégro-différentiel et semi-groupe de Feller sur un ouvert borné de
Problèmes concernant différentes classes d'équations intégro-différentielles non linéaires aux opérateurs polyvibrants
Product Integration for the Linear Transport Equation in Slab Geometry.
Properties of operators related to the Boltzmann collision term
Quelques applications de la positivité en théorie du transport
Quenching semidiscretizations in time of a nonlocal parabolic problem with Neumann boundary condition.
Recent results on the Boltzmann equation
In the last few years the theory of the nonlinear Boltzmann equation has witnessed a veritable turrent of contributions, spurred by the basic result of DiPerna and Lions. Here we wish to survey these results with particular attention to some recent developments.
Recovering a time- and space-dependent kernel in a hyperbolic integro-differential equation from a restricted Dirichlet-to-Neumann operator.
Regularity estimates via the entropy dissipation for the spatially homogeneous Boltzmann equation without cut-off.
We show that in the setting of the spatially homogeneous Boltzmann equation without cut-off, the entropy dissipation associated to a function f ∈ L1(RN) yields a control of √f in Sobolev norms as soon as f is locally bounded below. Under this additional assumption of lower bound, our result is an improvement of a recent estimate given by P.-L. Lions, and is optimal in a certain sense.
Regularizing a nonlinear integroparabolic Fokker--Planck equation with space-periodic solutions: existence of strong solutions.
Relaxation lengths and non-negative solutions in neutron transport
Remarks on Krasnoselskii bifurcation theorem
Richardson extrapolation and defect correction of mixed finite element methods for integro-differential equations in porous media
Asymptotic error expansions in the sense of -norm for the Raviart-Thomas mixed finite element approximation by the lowest-order rectangular element associated with a class of parabolic integro-differential equations on a rectangular domain are derived, such that the Richardson extrapolation of two different schemes and an interpolation defect correction can be applied to increase the accuracy of the approximations for both the vector field and the scalar field by the aid of an interpolation postprocessing...
Second order semilinear Volterra integrodifferential equation in Banach space
By using the theory of strongly continuous cosine families of linear operators in Banach space the existence of solutions of some semilinear second order Volterra integrodifferential equations in Banach spaces is proved. The results are applied to some integro-partial differential equations.
Second-order elliptic integro-differential equations : viscosity solutions' theory revisited
Semigroup Analysis of Structured Parasite Populations
Motivated by structured parasite populations in aquaculture we consider a class of size-structured population models, where individuals may be recruited into the population with distributed states at birth. The mathematical model which describes the evolution of such a population is a first-order nonlinear partial integro-differential equation of hyperbolic type. First, we use positive perturbation arguments and utilise results from the spectral...
Smoothing effect and regularity for evolution integrodifferential systems
Smoothness in fractional evolution equations and conservation laws