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Measure valued solutions of sub-linear diffusion equations with a drift term
sublinear diffusion concentration phenomena propagation of singularities gradient flows
2010/12/9
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...
Equilibration, generalized equipartition, and diffusion in dynamical Lorentz gases
Equilibration generalized equipartition diffusion dynamical Lorentz gases
2010/12/15
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...
Spatially regularized compressed sensing of diffusion MRI data
Spatially regularized compressed diffusion MRI data
2010/12/3
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...
Logarithmic Sobolev inequality for diffusion semigroups
Logarithmic Sobolev inequality Poincar´ e inequality Ornstein-Uhlenbeck semigroup
2010/12/8
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...
Alternating group iterative method for convection-diffusion equations
iterative method parallel computing alternating group
2010/9/13
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...
Ergodic approximation of the distribution of a stationary diffusion : rate of convergence
stochastic differential equation stationary process steady regime ergodic diffusion Central Limit Theorem Euler scheme
2010/11/26
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...
Local and Global Well-Posedness for Aggregation Equations and Patlak-Keller-Segel Models with Degenerate Diffusion
Local Global Well-Posedness Aggregation Equations Patlak-Keller-Segel Models Degenerate Diffusion
2010/12/6
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...
Elliptic operators with unbounded diffusion coefficients in Lp spaces
elliptic operators unbounded coefficients generation results analytic semigroups
2010/12/1
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 ...
Global existence of solutions for some coupled systems of reaction-diffusion equations
Reaction-Diffusion systems Global Existence Lyapunov Functional
2010/12/14
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...
On zero-sum Stochastic Differential Games with Jump-Diffusion driven state: A viscosity solution framework
Stochastic differential games L´ evy processes dynamic programming
2010/12/13
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...
Laguerre and Meixner symmetric functions, and infinite-dimensional diffusion processes
Laguerre Meixner symmetric functions infinite-dimensional diffusion processes
2010/12/3
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...
Large deviations of the empirical currents for a boundary driven reaction diffusion model
Large deviations Interacting particle system
2010/11/29
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...
Semi-Closed Form Cubature and Applications to Financial Diffusion Models
Ninomiya–Victoir method cubature method Monte Carlo simulation
2010/12/16
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.
Global Minimizers for Free Energies of Subcritical Aggregation Equations with Degenerate Diffusion
Global Minimizers Free Energies of Subcritical Aggregation Equations Degenerate Diffusion
2010/12/14
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...
Interaction between nonlinear diffusion and geometry of domain
nonlinear diffusion geometry of domain initial-boundary value problem
2010/12/15
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 ...