54 research outputs found
Caractérisation de classes de fonctions et analytiques sur une variété irrégulière à l'aide d'un opérateur différentiel
Analysis of direct segregated boundary-domain integral equations for variable-coefficient mixed bvps in exterior domains
This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2013 World Scientific Publishing.Direct segregated systems of boundary-domain integral equations are formulated for the mixed (Dirichlet–Neumann) boundary value problems for a scalar second-order divergent elliptic partial differential equation with a variable coefficient in an exterior three-dimensional domain. The boundary-domain integral equation system equivalence to the original boundary value problems and the Fredholm properties and invertibility of the corresponding boundary-domain integral operators are analyzed in weighted Sobolev spaces suitable for infinite domains. This analysis is based on the corresponding properties of the BVPs in weighted Sobolev spaces that are proved as well.The work was supported by the grant EP/H020497/1 \Mathematical analysis of localised boundary-domain integral equations for BVPs with variable coefficients" of the EPSRC, UK
Étude de l'analyticité et de la régularité Gevrey pour une classe de problèmes aux limites elliptiques et dégénérés
A priori convergence estimates for a rough Poisson-Dirichlet problem with natural vertical boundary conditions
Stents are medical devices designed to modify blood flow in aneurysm sacs, in
order to prevent their rupture. Some of them can be considered as a locally
periodic rough boundary. In order to approximate blood flow in arteries and
vessels of the cardio-vascular system containing stents, we use multi-scale
techniques to construct boundary layers and wall laws. Simplifying the flow we
turn to consider a 2-dimensional Poisson problem that conserves essential
features related to the rough boundary. Then, we investigate convergence of
boundary layer approximations and the corresponding wall laws in the case of
Neumann type boundary conditions at the inlet and outlet parts of the domain.
The difficulty comes from the fact that correctors, for the boundary layers
near the rough surface, may introduce error terms on the other portions of the
boundary. In order to correct these spurious oscillations, we introduce a
vertical boundary layer. Trough a careful study of its behavior, we prove
rigorously decay estimates. We then construct complete boundary layers that
respect the macroscopic boundary conditions. We also derive error estimates in
terms of the roughness size epsilon either for the full boundary layer
approximation and for the corresponding averaged wall law.Comment: Dedicated to Professor Giovanni Paolo Galdi 60' Birthda
Analysis of segregated boundary-domain integral equations for mixed variable-coefficient BVPs in exterior domains
This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2011 Birkhäuser Boston.Some direct segregated systems of boundary–domain integral equations (LBDIEs) associated with the mixed boundary value problems for scalar PDEs with variable coefficients in exterior domains are formulated and analyzed in the paper. The LBDIE equivalence to the original boundary value problems and the invertibility of the corresponding boundary–domain integral operators are proved in weighted Sobolev spaces suitable for exterior domains. This extends the results obtained by the authors for interior domains in non-weighted Sobolev spaces.The work was supported by the grant EP/H020497/1 ”Mathematical analysis of localised boundary-domain integral equations for BVPs with variable coefficients” of the EPSRC, UK
Global classical solutions for partially dissipative hyperbolic system of balance laws
This work is concerned with (-component) hyperbolic system of balance laws
in arbitrary space dimensions. Under entropy dissipative assumption and the
Shizuta-Kawashima algebraic condition, a general theory on the well-posedness
of classical solutions in the framework of Chemin-Lerner's spaces with critical
regularity is established. To do this, we first explore the functional space
theory and develop an elementary fact that indicates the relation between
homogeneous and inhomogeneous Chemin-Lerner's spaces. Then this fact allows to
prove the local well-posedness for general data and global well-posedness for
small data by using the Fourier frequency-localization argument. Finally, we
apply the new existence theory to a specific fluid model-the compressible Euler
equations with damping, and obtain the corresponding results in critical
spaces.Comment: 39 page
Integral potential method for a transmission problem with Lipschitz interface in R^3 for the Stokes and Darcy–Forchheimer–Brinkman PDE systems
The purpose of this paper is to obtain existence and uniqueness results in weighted Sobolev spaces for transmission problems for the non-linear Darcy-Forchheimer-Brinkman system and the linear Stokes system in two complementary Lipschitz domains in R3, one of them is a bounded Lipschitz domain with connected boundary, and the other one is the exterior Lipschitz domain R3 n. We exploit a layer potential method for the Stokes and Brinkman systems combined with a fixed point theorem in order to show the desired existence and uniqueness results, whenever the given data are suitably small in some weighted Sobolev spaces and boundary Sobolev spaces
Caractérisation de classes de fonctions par des itères d’opérateurs elliptiques dégénérés sur des ouverts irréguliers
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