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In this paper we study nonnegative, measure valued solutions of the initial value problem for one-dimensional drift-diffusion equations when the nonlinear diffusion is governed by an increasing C1 fu...
We prove approach to thermal equilibrium for the fully Hamiltonian dynamics of a dynamical Lorentz gas, by which we mean an ensemble of particles moving through a d-dimensional array of fixed soft sca...
Despite the relative recency of its inception, the theory of compres-sive sampling (aka compressed sensing) (CS) has already revolutionized multiple areas of applied sciences, a particularly important...
Through the main example of the Ornstein-Uhlenbeck semigroup, the Bakry-Emery criterion is presented as a main tool to get functional inequalities as Poincar´e or logarithmic Sobolev inequalitie...
In this paper, a symmetry implicit scheme for solving convectiondiffusion equations is presented with a kind of exponential type transformation. Based on the scheme a class of alternating group explic...
We extend to Lipschitz continuous functionals either of the true paths or of the Euler scheme with decreasing step of a wide class of Brownian ergodic diffusions, the Central Limit Theorems formally e...
Recently, there has been a wide interest in the study of aggregation equations and Patlak-Keller-Segel (PKS) models for chemotaxis with degenerate diffusion. The focus of this paper is the unification...
In this paper we prove that, under suitable assumptions on > 0, the operator L = (1+|x| ) admits realizations generating contraction or analytic semigroups in Lp(RN). For some values of , we also ...
The aim of this work is to study the global existence of solutions for some coupled systems of reaction diffusion which describe the spread within a population of infectious disease. We consider a tri...
A zero-sum differential game with controlled jump-diffusion driven state is considered, and studied using a combination of dynamic programming and viscosity solution techniques. We prove, under certai...
The Laguerre symmetric functions introduced in the note are indexed by arbitrary partitions and depend on two continuous parameters. The top degree homogeneous component of every Laguerre symmetric fu...
We derive a large deviation principle for the empirical currents of lattice gas dynamics which combine a fast stirring mechanism (Symmetric Simple Exclusion Process) and creation/annihilation mechanis...
Cubature methods, a powerful alternative to Monte Carlo due to Kusuoka [Adv. Math. Econ. 6, 69–83, 2004] and Lyons–Victoir [Proc. R. Soc.Lond. Ser.
We prove the existence of non-trivial global minimizers of a class of free energies related to aggregation equations with degenerate diffusion on Rd. Such equations arise in mathematical biology as mo...
Let be a domain in RN, where N ≥ 2 and @ is not necessarily bounded. We consider nonlinear diffusion equations of the form @tu = (u). Let u = u(x, t) be the solution of either the initial-boundary ...

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