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Total overlapping Schwarz' preconditioners for elliptic problems

Faker Ben Belgacem, Nabil Gmati, Faten Jelassi (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

A variant of the Total Overlapping Schwarz (TOS) method has been introduced in [Ben Belgacem et al., C. R. Acad. Sci., Sér. 1 Math. 336 (2003) 277–282] as an iterative algorithm to approximate the absorbing boundary condition, in unbounded domains. That same method turns to be an efficient tool to make numerical zooms in regions of a particular interest. The TOS method enjoys, then, the ability to compute small structures one wants to capture and the reliability to obtain the behavior of the solution...

Total overlapping Schwarz' preconditioners for elliptic problems

Faker Ben Belgacem, Nabil Gmati, Faten Jelassi (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

A variant of the Total Overlapping Schwarz (TOS) method has been introduced in [Ben Belgacem et al., C. R. Acad. Sci., Sér. 1 Math.336 (2003) 277–282] as an iterative algorithm to approximate the absorbing boundary condition, in unbounded domains. That same method turns to be an efficient tool to make numerical zooms in regions of a particular interest. The TOS method enjoys, then, the ability to compute small structures one wants to capture and the reliability to obtain the...

Toward a mathematical analysis for a model of suspension flowing down an inclined plane

Matsue, Kaname, Tomoeda, Kyoko (2017)

Proceedings of Equadiff 14

We consider the Riemann problem of the dilute approximation equations with spatiotemporally dependent volume fractions from the full model of suspension, in which the particles settle to the solid substrate and the clear liquid film flows over the sediment [Murisic et al., J. Fluid. Mech. 717, 203–231 (2013)]. We present a method to find shock waves, rarefaction waves for the Riemann problem of this system. Our method is mainly based on [Smoller, Springer-Verlag, New York, second edition, (1994)]....

Toward the sinc-Galerkin method for the Poisson problem in one type of curvilinear coordinate domain.

Yamamoto, Toshihiro (2006)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Towards a two-scale calculus

Augusto Visintin (2006)

ESAIM: Control, Optimisation and Calculus of Variations

We define and characterize weak and strong two-scale convergence in Lp, C0 and other spaces via a transformation of variable, extending Nguetseng's definition. We derive several properties, including weak and strong two-scale compactness; in particular we prove two-scale versions of theorems of Ascoli-Arzelà, Chacon, Riesz, and Vitali. We then approximate two-scale derivatives, and define two-scale convergence in spaces of either weakly or strongly differentiable functions. We also derive...

Towards finite-gap integration of the Inozemtsev model.

Takemura, Kouichi (2007)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Towards the Cauchy problem for the Laplace equation

Dinh Hào, Tran Van, Rudolf Gorenflo (1992)

Banach Center Publications

T-Periodic Solutions of Time Dependent Hamiltonian Systems with a Potential Vanishing at Infinity.

Klaus Thews (1980/1981)

Manuscripta mathematica

T-p(x)-solutions for nonlinear elliptic equations with an L¹-dual datum

El Houssine Azroul, Abdelkrim Barbara, Meryem El Lekhlifi, Mohamed Rhoudaf (2012)

Applicationes Mathematicae

We establish the existence of a T-p(x)-solution for the p(x)-elliptic problem $- d i v (a (x, u, \nabla u)) + g (x, u) = f - d i v F$ in Ω, where Ω is a bounded open domain of $ℝ^{N}$ , N ≥ 2 and $a : Ω \times ℝ \times ℝ^{N} \to ℝ^{N}$ is a Carathéodory function satisfying the natural growth condition and the coercivity condition, but with only a weak monotonicity condition. The right hand side f lies in L¹(Ω) and F belongs to $\prod_{i = 1}^{N} L^{p^{'} (\cdot)} (Ω)$ .

Trace class pseudodifferential calculus with operator valued symbols and unusual index formulas

Grigori Rozenblum (2000/2001)

Séminaire Équations aux dérivées partielles

For several classes of pseudodifferential operators with operator-valued symbol analytic index formulas are found. The common feature is that usual index formulas are not valid for these operators. Applications are given to pseudodifferential operators on singular manifolds.

Trace imbeddings for $T$ -sets and application to Neumann-Dirichlet problems with measures included in the boundary data

Andrée Decarreau, Jin Liang, Jean-Michel Rakotoson (1996)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Trace Properties of the Dirichlet Laplacian.

E.B. Davies (1984/1985)

Mathematische Zeitschrift

Trace theorem on the Heisenberg group

Hajer Bahouri, Jean-Yves Chemin, Chao-Jiang Xu (2009)

Annales de l’institut Fourier

We prove in this work the trace and trace lifting theorem for Sobolev spaces on the Heisenberg groups for hypersurfaces with characteristics submanifolds.

Traces and fine properties of a $B D$ class of vector fields and applications

Luigi Ambrosio, Gianluca Crippa, Stefania Maniglia (2005)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Traces and quasi-traces on the Boutet de Monvel algebra

Gerd Grubb, Elmar Schrohe (2004)

Annales de l’institut Fourier

We construct an analogue of Kontsevich and Vishik’s canonical trace for pseudodifferential boundary value problems in the Boutet de Monvel calculus on compact manifolds with boundary. For an operator $A$ in the calculus (of class zero), and an auxiliary operator $B$ , formed of the Dirichlet realization of a strongly elliptic second- order differential operator and an elliptic operator on the boundary, we consider the coefficient $C_{0} (A, B)$ of ${(- λ)}^{- N}$ in the asymptotic expansion of the resolvent trace $Tr (A {(B - λ)}^{- N})$ (with $N$ large)...

Traces and the F. and M. Riesz theorem for vector fields

Shiferaw Berhanu, Jorge Hounie (2003)

Annales de l’institut Fourier

This work studies conditions that insure the existence of weak boundary values for solutions of a complex, planar, smooth vector field $L$ . Applications to the F. and M. Riesz property for vector fields are discussed.

Traces of pluriharmonic functions

Paolo de Bartolomeis, Giuseppe Tomassini (1981)

Compositio Mathematica

Traduzione in equazioni integrali di un problema analogo al problema biarmonico fondamentale

Bruno Pini (1953)

Rendiconti del Seminario Matematico della Università di Padova

Transfer matrices and transport for Schrödinger operators

François Germinet, Alexander Kiselev, Serguei Tcheremchantsev (2004)

Annales de l’institut Fourier

We provide a general lower bound on the dynamics of one dimensional Schrödinger operators in terms of transfer matrices. In particular it yields a non trivial lower bound on the transport exponents as soon as the norm of transfer matrices does not grow faster than polynomially on a set of energies of full Lebesgue measure, and regardless of the nature of the spectrum. Applications to Hamiltonians with a) sparse, b) quasi-periodic, c) random decaying potential are provided....

Transfer of boundary conditions for difference equations

Emil Vitásek (2000)

Applications of Mathematics

It is well-known that the idea of transferring boundary conditions offers a universal and, in addition, elementary means how to investigate almost all methods for solving boundary value problems for ordinary differential equations. The aim of this paper is to show that the same approach works also for discrete problems, i.e., for difference equations. Moreover, it will be found out that some results of this kind may be obtained also for some particular two-dimensional problems.

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