Existence and uniqueness of almost everywhere solutions of nonlocal problems to functional partial differential systems in diagonal form are investigated. The proof is based on the characteristics and fixed point methods.
Nous exposons un exemple de non unicité du problème de Cauchy non caractéristique pour l’équation de transport associé à un champ de vecteurs borné, à divergence nulle et néanmoins à coefficients peu réguliers
Our aim is to find roots of the non-unique behavior of gases which can be observed in certain axisymmetric nozzle geometries under special flow regimes. For this purpose, we use several versions of the compressible Euler equations. We show that the main reason for the non-uniqueness is hidden in the energy decomposition into its internal and kinetic parts, and their complementary behavior. It turns out that, at least for inviscid compressible flows, a bifurcation can occur only at flow regimes with...
∗The author was partially supported by M.U.R.S.T. Progr. Nazionale “Problemi Non Lineari...”In this work we analyse the nonlinear Cauchy problem (∂tt − ∆)u(t, x) = ( λg + O(1/(1 + t + |x|)^a) ) ) ∇t,x u(t, x), ∇t,x u(t, x) ), whit initial data u(0, x) = e u0 (x), ut (0, x) = e u1 (x). We assume a ≥ 1, x ∈ R^n (n ≥ 3) and g the matrix related to the Minkowski space. It can be considerated a pertubation of the case when the quadratic term has constant coefficient λg (see Klainerman [6]) We...
We prove almost optimal local well-posedness for the coupled Dirac–Klein–Gordon (DKG) system of equations in dimensions. The proof relies on the null structure of the system, combined with bilinear spacetime estimates of Klainerman–Machedon type. It has been known for some time that the Klein–Gordon part of the system has a null structure; here we uncover an additional null structure in the Dirac equation, which cannot be seen directly, but appears after a duality argument.
The Shape-From-Shading (SFS) problem is a fundamental and classic problem in computer vision. It amounts to compute the 3-D depth of objects in a single given 2-D image. This is done by exploiting information about the illumination and the image brightness. We deal with a recent model for Perspective SFS (PSFS) for Lambertian surfaces. It is defined by a Hamilton–Jacobi equation and complemented by state constraints boundary conditions. In this paper we investigate and compare three state-of-the-art...
In this paper we introduce a coupled systems of kinetic equations for the linearized Carleman model. We then study the existence theory and the asymptotic behaviour of the resulting coupled problem. In order to solve the coupled problem we propose to use the time marching algorithm. We then develop a convergence theory for the resulting algorithm. Numerical results confirming the theory are then presented.
The purpose of this article is the analysis and the development of Eulerian multi-fluid models to describe the evolution of the mass density of evaporating liquid sprays. First, the classical multi-fluid model developed in [Laurent and Massot, Combust. Theor. Model.5 (2001) 537–572] is analyzed in the framework of an unsteady configuration without dynamical nor heating effects, where the evaporation process is isolated, since it is a key issue. The classical multi-fluid method consists then in...
A new set of nonlocal boundary conditions is proposed for the higher modes of the 3D inviscid primitive equations. Numerical schemes using the splitting-up method are proposed for these modes. Numerical simulations of the full nonlinear primitive equations are performed on a nested set of domains, and the results are discussed.