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1.
We deal with the numerical solution of a scalar nonstationary nonlinear convection–diffusion equation. We employ a combination
of the discontinuous Galerkin finite element method for the space semi-discretization and the k-step backward difference formula for the time discretization. The diffusive and stabilization terms are treated implicitly
whereas the nonlinear convective term is treated by a higher order explicit extrapolation method, which leads to the necessity
to solve only a linear algebraic problem at each time step. We analyse this scheme and derive a priori asymptotic error estimates
in the discrete L
∞(L
2)-norm and the L
2(H
1)-seminorm with respect to the mesh size h and time step τ for k = 2,3. Numerical examples verifying the theoretical results are presented.
This work is a part of the research project MSM 0021620839 financed by the Ministry of Education of the Czech Republic and
was partly supported by the Grant No. 316/2006/B-MAT/MFF of the Grant Agency of the Charles University Prague. The research
of M. Vlasák was supported by the project LC06052 of the Ministry of Education of the Czech Republic (Jindřich Nečas Center
for Mathematical Modelling). 相似文献
2.
A new approach to boundary trace inequalities for Sobolev functions is presented, which reduces any trace inequality involving
general rearrangement-invariant norms to an equivalent, considerably simpler, one-dimensional inequality for a Hardy-type
operator. In particular, improvements of classical boundary trace embeddings and new optimal trace embeddings are derived.
This research was partially supported by the Italian research project “Geometric properties of solutions to variational problems”
of GNAMPA (INdAM) 2006, by the research project MSM 0021620839 of the Czech Ministry of Education, by grants 201/03/0935,
201/05/2033 and 201/07/0388 of the Grant Agency of the Czech Republic and by the Nečas Center for Mathematical Modeling project
no. LC06052 financed by the Czech Ministry of Education. 相似文献
3.
Sebastian Król 《Semigroup Forum》2009,79(2):369-376
We show that every contractive C
0-semigroup on a separable, infinite-dimensional Hilbert space X can be approximated by unitary C
0-groups in the weak operator topology uniformly on compact subsets of ℝ+. As a consequence we get a new characterization of a bounded H
∞-calculus for the negatives of generators of bounded holomorphic semigroups. Applications of our results to the study of a
topological structure of the set of (almost) weakly stable contractive C
0-semigroups on X are also discussed.
The author was partially supported by the Marie Curie “Transfer of Knowledge” programme, project “TODEQ”, and by a MNiSzW
grant Nr. N201384834. 相似文献
4.
The Sz.-Nagy-FoiaŞ functional model for completely non-unitary contractions is extended to completely non-coisometric sequences
of bounded operatorsT = (T1,...,T
d) (d finite or infinite) on a Hilbert space, with bounded characteristic functions. For this class of sequences, it is shown
that the characteristic function θT is a complete unitary invariant.
We obtain, as the main result, necessary and sufficient conditions for a bounded multi-analytic operator on Fock spaces to
coincide with the characteristic function associated with a completely non-coisometric sequence of bounded operators on a
Hilbert space.
Research supported in part by a COBASE grant from the National Research Council.
The first author was partially supported by a grant from Ministerul Educaţiei Şi Cercetarii.
The second author was partially supported by a National Science Foundation grant. 相似文献
5.
In this paper, we prove that the K?hler–Ricci flow converges to a K?hler–Einstein metric when E
1 energy is small. We also prove that E
1 is bounded from below if and only if the K-energy is bounded from below in the canonical class.
The first named author is partially supported by a NSF grant, while the third author was partially supported by a NSF supplement
grant. 相似文献
6.
We consider the boundary value problem Δu+⋎x⋎2α
u
p
=0, α>0, in the unit ballB with homogeneous Dirichlet boundary condition andp a large exponent. We find a condition which ensures the existence of a positive solutionu
p
concentrating outside the origin atk symmetric points asp goes to +∞. The same techniques lead also to a more general result on general domains. In particular, we find that concentration
at the origin is always possible, provided α⊄IN.
The first author is supported by M.U.R.S.T., project “Variational methods and nonlinear differential equations” and a PIMS
Postdoctoral Fellowship.
The second author is supported by M.U.R.S.T., project “Metodi variazionali e topologici nello studio di fenomeni non lineari.”
The third author is supported by an Earmarked Grant from RGC of HK. 相似文献
7.
Rodolfo Salvi 《Annali dell'Universita di Ferrara》2000,46(1):251-266
In this paper we are concerned with the flow of a viscous, incompressible fluid in a bounded, three-dimensional region Ω with
free surface boundary conditions. Using a method introduced by the author, that consider a two-fluid system in which the atmosphere
or the vacuum is considered as a second fluid, separated from the first one by a free interface Γ(t), we prove existence of a kind of weak solution that we call quasi-weak solution.
Work supported by Progetto Murst n. 9801262841. 相似文献
Sunto In questo lavoro studiamo il moto di un fluido viscoso e incomprimibile in una regione limitata tridimensionale Ω, con condizioni al contorno di superficie libera. Utilizzando un metodo, dovuto all’autore, che consiste nel considerare l’atmosfera o il vuoto come un secondo fluido, separato dal primo da un’interfaccia mobile Γ(t), dimostriamo l’esistenza di una sorta di soluzione debole, denominata soluzione quasi-debole.
Work supported by Progetto Murst n. 9801262841. 相似文献
8.
DunYanYAN GuoEnHU 《数学学报(英文版)》2005,21(1):209-214
In this paper, the authors discuss a class of multilinear singular integrals and obtain that the operators are bounded from H^1(R^n) to weak L^1(R^n). Using this result, we can directly prove a main theorem in [5]. 相似文献
9.
A universal algebra isaffine complete if all functions satisfying the Substitution Property are polynomials (composed of the basic operations and the elements of the algebra). In 1962, the first author proved that a bounded distributive lattice is affine complete if and only if it does not contain a proper Boolean interval. Recently, M. Ploica generalized this result to arbitrary distributive lattices.In this paper, we introduce a class of functions on a latticeL, we call themID-polynomials, that derive from polynomials on the ideal lattice (resp., dual ideal lattice) ofL; they are isotone functions and satisfy the Substitution Property. We prove that for a distributive latticeL, all unary functions with the Substitution Property are ID-polynomials if and only ifL contains no proper Boolean interval.The research of the first author was supported by the NSERC of Canada. The research of the second author was supported by the Hungarian National Foundation for Scientific Research, under Grant No. 1903. 相似文献
10.
In this paper, we characterize classes of matrix transformations from BK spaces into spaces of bounded sequences and their
subclasses of infinite matrices that define compact operators. Furthermore, using these results and the solvability of certain
infinite linear systems we give necessary and sufficient conditions for A to be a compact operator on spaces that are strongly α-bounded or summable.
Research is supported by the German DAAD foundation (German Academic Exchange Service), the University of Le Havre and the
research project #1232 of the Serbian Ministry of Science, Technology and Development. 相似文献
11.
We study the possibility of splitting any bounded analytic function ƒ with singularities in a closed set E ⋃ F as a sum of two bounded analytic functions with singularities in E and F respectively. We obtain some results under geometric restrictions on the sets E and F and we provide some examples showing the sharpness of the positive results.
The first author is partially supported by RFBR grant #06-01-00313 and by the grant for Leading Scientific Schools #NSH-2266-2003.1.
The last author is supported by DGICYT grant MTM2005-08984-C02-02 and the CIRIT grant 2005SGR00611. 相似文献
12.
U. Bruzzo 《Israel Journal of Mathematics》1992,80(1-2):161-169
We show that Berezin integration can be consistently defined on a supermanifold (M, A) of the DeWitt type. The resulting integral is a real-valued functional on the space of compactly supported global sections
of the Berezinian sheaf of (M, A).
Research partly supported by ‘Gruppo Nazionale per la Fisica Matematica’ of CNR and by the Italian Ministry for the Universities
and Scientific and Technological Research through the research project ‘Metodi geometrici in relatività e teorie di campo.’ 相似文献
13.
Josef Daněček Eugen Viszus 《NoDEA : Nonlinear Differential Equations and Applications》2009,16(2):189-211
We discuss the interior C
0,γ-everywhere regularity for minimizers of quasilinear functionals of the type
where VMO dependence on the variable x and continuous dependence on the variable u are supposed.
J. Daněček was supported by the research project MSM 0021630511, E. Viszus was supported by the research project Slovak Grant
Agency No.1/0098/08. 相似文献
14.
On the Proper Homotopy Invariance of the Tucker Property 总被引:1,自引:0,他引:1
Daniele Ettore OTERA 《数学学报(英文版)》2007,23(3):571-576
A non-compact polyhedron P is Tucker if, for any compact subset K begong to P, the fundamental group π1 (P - K) is finitely generated. The main result of this note is that a manifold which is proper homotopy equivalent to a Tucker polyhedron is Tucker. We use Poenaru's theory of the equivalence relations forced by the singularities of a non-degenerate simplicial map. 相似文献
15.
Nešetřil and Sopena introduced the concept of oriented game chromatic number. They asked whether the oriented game chromatic
number of partial k-trees was bounded. Here we answer their question positively.
Received: January 12, 2001 Final version received: February 25, 2002 相似文献
16.
Matsuoka showed an asymptotic formula for the coefficients of the Laurent expansion of ζ (s) at s = 1. In the present paper we extend this result to a large class of Dirichlet series which was first studied by Chandrasekharan
and Narasimhan. Our proofs are based on a saddle point argument and use the fact that the Dirichlet series under consideration
admit a functional equation.
The second author was supported by the FWF project S381O. 相似文献
17.
We present a distribution-free model of incomplete-information games, both with and without private information, in which
the players use a robust optimization approach to contend with payoff uncertainty. Our ``robust game' model relaxes the assumptions
of Harsanyi's Bayesian game model, and provides an alternative distribution-free equilibrium concept, which we call ``robust-optimization
equilibrium,' to that of the ex post equilibrium. We prove that the robust-optimization equilibria of an incomplete-information game subsume the ex post equilibria of the game and are, unlike the latter, guaranteed to exist when the game is finite and has bounded payoff uncertainty
set. For arbitrary robust finite games with bounded polyhedral payoff uncertainty sets, we show that we can compute a robust-optimization
equilibrium by methods analogous to those for identifying a Nash equilibrium of a finite game with complete information. In
addition, we present computational results.
The research of the author was partially supported by a National Science Foundation Graduate Research Fellowship and by the
Singapore-MIT Alliance.
The research of the author was partially supported by the Singapore-MIT Alliance. 相似文献
18.
We revisit the boundedness of Hankel and Toeplitz operators acting on the Hardy space H
1 and give a new proof of the old result stating that the Hankel operator H
a
is bounded if and only if a has bounded logarithmic mean oscillation. We also establish a sufficient and necessary condition for H
a
to be compact on H
1. The Fredholm properties of Toeplitz operators on H
1 are studied for symbols in a Banach algebra similar to C + H
∞ under mild additional conditions caused by the differences in the boundedness of Toeplitz operators acting on H
1 and H
2.
The first author was partially supported by the European Commission IHP Network “Harmonic Analysis and Related Problems” (Contract
Number: HPRN-CT-2001-00273-HARP) and by the Greek Research Program “Pythagoras 2” (75% European funds and 25 National funds).
The second author was fully supported by the European Commission IHP Network “Harmonic Analysis and Related Problems” (Contract
Number: HPRN-CT-2001-00273-HARP) while he visited the first author at the University of Crete and later by the Academy of
Finland Project 207048. 相似文献
19.
If (Ω,Σ) is a measurable space and X a Banach space, we provide sufficient conditions on Σ and X in order to guarantee that bvca(Σ, X) the Banach space of all X-valued countably additive measures of bounded variation equipped with the variation norm, contains a copy of c0 if and only if X does.
This work was supported by the project MTM2005-01182 of the Spanish Ministry of Education and Science, co-financed by the
European Community (Feder projects). 相似文献
20.
We give necessary and sufficient conditions for the (bounded) law of the iterated logarithm for U-statistics in Hilbert spaces. As a tool we also develop moment and tail estimates for canonical Hilbert-space valued U-statistics of arbitrary order, which are of independent interest.
R. Adamczak’s research partially supported by MEiN Grant 2 PO3A 019 30.
R. Latała’s research partially supported by MEiN Grant 1 PO3A 012 29. 相似文献