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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...
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...
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)]....
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...
We establish the existence of a T-p(x)-solution for the p(x)-elliptic problem
in Ω,
where Ω is a bounded open domain of , N ≥ 2 and 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 .
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.
We prove in this work the trace and trace lifting theorem for Sobolev spaces on the Heisenberg groups for hypersurfaces with characteristics submanifolds.
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 in the calculus (of class zero), and an
auxiliary operator , formed of the Dirichlet realization of a strongly elliptic second-
order differential operator and an elliptic operator on the boundary, we consider the
coefficient of in the asymptotic expansion of the resolvent
trace (with large)...
This work studies conditions that insure the existence of weak boundary values for
solutions of a complex, planar, smooth vector field . Applications to the F. and M.
Riesz property for vector fields are discussed.
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....
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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