Propagation of analytic singularities for the Schrödinger Equation
Propagation of analyticity of solutions to the Cauchy problem for Kirchhoff type equations
We shall give the local in time existence of the solutions in Gevrey classes to the Cauchy problem for Kirhhoff equations of -laplacian type and investigate the propagation of analyticity of solutions for real analytic deta. When , his equation as the global real analytic solution for the real analytic initial data.
Propagation of analyticity of the solutions to the Cauchy problem for nonlinear symmetrizable systems
Propagation of chaos for Burgers' equation
Propagation of chaos for the 2D viscous vortex model
We consider a stochastic system of particles, usually called vortices in that setting, approximating the 2D Navier-Stokes equation written in vorticity. Assuming that the initial distribution of the position and circulation of the vortices has finite (partial) entropy and a finite moment of positive order, we show that the empirical measure of the particle system converges in law to the unique (under suitable a priori estimates) solution of the 2D Navier-Stokes equation. We actually prove a slightly...
Propagation of delayed lattice differential equations without local quasimonotonicity
This paper is concerned with the traveling wave solutions and asymptotic spreading of delayed lattice differential equations without quasimonotonicity. The spreading speed is obtained by constructing auxiliary equations and using the theory of lattice differential equations without time delay. The minimal wave speed of invasion traveling wave solutions is established by investigating the existence and nonexistence of traveling wave solutions.
Propagation of electromagnetic waves in non-homogeneous media
We consider electromagnetic waves propagating in a periodic medium characterized by two small scales. We perform the corresponding homogenization process, relying on the modelling by Maxwell partial differential equations.
Propagation of Gevrey regularity over long times for the fully discrete Lie Trotter splitting scheme applied to the linear Schrödinger equation
In this paper, we study the linear Schrödinger equation over the d-dimensional torus, with small values of the perturbing potential. We consider numerical approximations of the associated solutions obtained by a symplectic splitting method (to discretize the time variable) in combination with the Fast Fourier Transform algorithm (to discretize the space variable). In this fully discrete setting, we prove that the regularity of the initial datum is preserved over long times, i.e. times that are...
Propagation of Growth Uncertainty in a Physiologically Structured Population
In this review paper we consider physiologically structured population models that have been widely studied and employed in the literature to model the dynamics of a wide variety of populations. However in a number of cases these have been found inadequate to describe some phenomena arising in certain real-world applications such as dispersion in the structure variables due to growth uncertainty/variability. Prompted by this, we described two recent...
Propagation of moments and regularity for the 3-dimensional Vlasov-Poisson system.
Propagation of perturbations in thin capillary film equations with nonlinear diffusion and convection.
Propagation of singularities along gliding rays
Propagation of singularities and local solvability in Gevrey classes
Propagation of singularities and maximal functions in the plane.
Propagation of Singularities and Related Problems of Solidification
Propagation of singularities for a first order semi-linear system in
Propagation of singularities for interior mixed hyperbolic problem
Propagation of singularities for linear partial differential equations and reflections at a boundary
Propagation of Singularities for Non Real Pseudo-Differential Operators
Propagation of singularities for the wave equation on manifolds with corners
In this talk we describe the propagation of and Sobolev singularities for the wave equation on manifolds with corners equipped with a Riemannian metric . That is, for , , and solving with homogeneous Dirichlet or Neumann boundary conditions, we show that is a union of maximally extended generalized broken bicharacteristics. This result is a counterpart of Lebeau’s results for the propagation of analytic singularities on real analytic manifolds with appropriately stratified boundary,...