共查询到20条相似文献,搜索用时 31 毫秒
1.
Roland Schnaubelt 《Journal of Evolution Equations》2001,1(1):19-37
We study the long-term behaviour of the parabolic evolution equation $\[u'(t)=A(t)u(t)+f(t), t>s,\quad u(s)=x. \]$\[u'(t)=A(t)u(t)+f(t), t>s,\quad u(s)=x. \] If A(t) A(t) converges to a sectorial operator A with s(A)?i \Bbb R = ? \sigma(A)\cap i \Bbb R =\emptyset as t?¥ t\to\infty , then the evolution family solving the homogeneous problem has exponential dichotomy. If also f(t)? f¥ f(t)\to f_\infty , then the solution u converges to the 'stationary solution at infinity', i.e., limt?¥u(t) = -A\sp-1f¥=:u¥, limt?¥u¢(t)=0, limt?¥A(t)u(t)=Au¥. \lim_{t\to\infty}u(t)= -A\sp{-1}f_\infty=:u_\infty, \qquad \lim_{t\to\infty}u'(t)=0, \qquad \lim_{t\to\infty}A(t)u(t)=Au_\infty. . 相似文献
2.
Bruno Franchi Maria Carla Tesi 《NoDEA : Nonlinear Differential Equations and Applications》2001,8(4):363-387
In this paper we present homogenization results for elliptic degenerate differential equations describing strongly anisotropic media. More precisely, we study the limit as e? 0 \epsilon \to 0 of the following Dirichlet problems with rapidly oscillating periodic coefficients:¶¶ . \cases {{ -div(\alpha(\frac{x}{\epsilon}}, \nabla u) A(\frac{x}{\epsilon}) \nabla u) = f(x) \in L^{\infty}(\Omega) \atop u = 0 su \eth\Omega\ } ¶¶where, p > 1, a: \Bbb Rn ×\Bbb Rn ? \Bbb R, a(y,x) ? áA(y)x,x?p/2-1, A ? Mn ×n(\Bbb R) p>1, \quad \alpha : \Bbb R^n \times \Bbb R^n \to \Bbb R, \quad \alpha(y,\xi) \approx \langle A(y)\xi,\xi \rangle ^{p/2-1}, A \in M^{n \times n}(\Bbb R) , A being a measurable periodic matrix such that At(x) = A(x) 3 0A^t(x) = A(x) \ge 0 almost everywhere.¶¶The anisotropy of the medium is described by the following structure hypothesis on the matrix A:¶¶l2/p(x) |x|2 £ áA(x)x,x? £ L 2/p(x) |x|2, \lambda^{2/p}(x) |\xi|^2 \leq \langle A(x)\xi,\xi \rangle \leq \Lambda ^{2/p}(x) |\xi|^2, ¶¶where the weight functions l \lambda and L \Lambda (satisfying suitable summability assumptions) can vanish or blow up, and can also be "moderately" different. The convergence to the homogenized problem is obtained by a classical compensated compactness argument, that had to be extended to two-weight Sobolev spaces. 相似文献
3.
If the longitudinal line method is applied to the Cauchy problem ut = uxx, u(0, x) = u0(x) with a bounded function u0, one is led to a linear initial value problem v¢(t)=A v(t), v(0)=wv'(t)=A v(t),\, v(0)=w in l¥ (\Bbb Z)l^\infty (\Bbb Z). Using Banach limit techniques we study the asymptotic behaviour of the solutions of these problems as t tends to infinity. 相似文献
4.
Let X be a smooth algebraic surface, L ? Pic(X) L \in \textrm{Pic}(X) and H an ample divisor on X. Set MX,H(2; L, c2) the moduli space of rank 2, H-stable vector bundles F on X with det(F) = L and c2(F) = c2. In this paper, we show that the geometry of X and of MX,H(2; L, c2) are closely related. More precisely, we prove that for any ample divisor H on X and any L ? Pic(X) L \in \textrm{Pic}(X) , there exists
n0 ? \mathbbZ n_0 \in \mathbb{Z} such that for all
n0 \leqq c2 ? \mathbbZ n_0 \leqq c_2 \in \mathbb{Z} , MX,H(2; L, c2) is rational if and only if X is rational. 相似文献
5.
B. Green 《Geometric And Functional Analysis》2002,12(3):584-597
We prove several results concerning arithmetic progressions in sets of integers. Suppose, for example, that a \alpha and b \beta are positive reals, that N is a large prime and that C,D í \Bbb Z/N\Bbb Z C,D \subseteq {\Bbb Z}/N{\Bbb Z} have sizes gN \gamma N and dN \delta N respectively. Then the sumset C + D contains an AP of length at least ec ?{log} N e^{c \sqrt{\rm log} N} , where c > 0 depends only on g \gamma and d \delta . In deriving these results we introduce the concept of hereditary non-uniformity (HNU) for subsets of \Bbb Z/N\Bbb Z {\Bbb Z}/N{\Bbb Z} , and prove a structural result for sets with this property. 相似文献
6.
L. Brevdo 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2001,54(5):397-420
We show that a homogeneous elastic ice layer of finite thickness and infinite horizontal extension floating on the surface of a homogeneous water layer of finite depth possesses a countable unbounded set of of resonant frequencies. The water is assumed to be compressible, the viscous effects are neglected in the model. Responses of this water-ice system to spatially localized harmonic in time perturbations with the resonant frequencies grow at least as ?t\sqrt{t} in the two-dimensional (2-D) case and at least as lnt in the three-dimensional (3-D) case, when time t?¥.t\to\infty. The analysis is based on treating the 3-D linear stability problem by applying the Laplace-Fourier transform and reducing the consideration to the 2-D case. The dispersion relation for the 2-D problem D(k,w) = 0,{D}(k,\omega) = 0, obtained previously by Brevdo and Il'ichev [10], is treated analytically and also computed numerically. Here k is a wavenumber, and w\omega is a frequency. It is proved that the system D(k,w) = 0, Dk(k,w) = 0{D}(k,\omega) = 0, {D}_k(k,\omega) = 0 possesses a countable unbounded set of roots (k, w) = (0,wn), n ? \Bbb Z(k, \omega) = (0,\omega_n), n\in\Bbb Z with Im wn = 0.\rm{Im}\ \omega_n = 0. Then the analysis of Brevdo [6], [7], [8], [9], which showed the existence of resonances in a homogeneous elastic waveguide, is applied to show that similar resonances exist in the present water-ice model. We propose a resonant mechanism for ice-breaking. It is based on destabilizing the floating ice layer by applying localized harmonic perturbations, with a moderate amplitude and at a resonant frequency. 相似文献
7.
M. Hasson 《Archiv der Mathematik》2001,76(4):283-291
Let W ì \Bbb Rn\Omega \subset {\Bbb R}^n be a smooth domain and let u ? C0(W).u \in C^0(\Omega ). A classical result of potential theory states that¶¶-òSr([`(x)]) u(x)ds(x)=u([`(x)])-\kern-5mm\int\limits _{S_{r}(\bar x)} u(x)d\sigma (x)=u(\bar x)¶¶for every [`(x)] ? W\bar x\in \Omega and r > 0r>0 if and only if¶¶Du=0 in W.\Delta u=0 \hbox { in } \Omega.¶¶Here -òSr([`(x)]) u(x)ds(x)-\kern-5mm\int\limits _{S_{r}(\bar x)} u(x)d\sigma (x) denotes the average of u on the sphere Sr([`(x)])S_r(\bar x) of center [`(x)]\bar x and radius r. Our main result, which is a "localized" version of the above result, states:¶¶Theorem. Let u ? W2,1(W)u\in W^{2,1}(\Omega ) and let x ? Wx\in \Omega be a Lebesgue point of Du\Delta u such that¶¶-òSr([`(x)]) u d s- a = o(r2)-\kern-5mm\int\limits _{S_{r}(\bar x)} u d \sigma - \alpha =o(r^2)¶¶for some a ? \Bbb R\alpha \in \Bbb R and all sufficiently small r > 0.r>0. Then¶¶Du(x)=0.\Delta u(x)=0. 相似文献
8.
W. Müller 《Geometric And Functional Analysis》2000,10(5):1118-1170
Let G be a reductive algebraic group defined over \Bbb Q {\Bbb Q} . Let P, P' be parabolic subgroups of G, defined over \Bbb Q {\Bbb Q} , and let _boxclose_boxclose, a_P') t \in W({\frak a}_{P}, {\frak a}_{P'}) . In this paper we study the intertwining operator MP¢|P(t,l), l ? \frak a*P,\Bbb C M_{P' \vert P}(t,\lambda),\,\lambda \in {\frak a}^*_{P,{\Bbb C}} , acting in corresponding spaces of automorphic forms. One of the main results states that each matrix coefficient of MP¢|P(t,l) M_{P' \vert P}(t,\lambda) is a meromorphic function of order £ n + 1 \le n + 1 , where n = dim G. Using this result, we further investigate the rank one intertwining operators, in particular, we study the distribution of their poles. 相似文献
9.
Wolfgang M. Ruppert 《Archiv der Mathematik》1999,72(4):278-281
We give an elementary argument for the well known fact that the endomorphism algebra
End(A)?\Bbb Q {\rm {End}}(A)\otimes {\Bbb Q } of a simple complex abelian surface A can neither be an imaginary quadratic field nor a definite quaternion algebra. Another consequence of our argument is that a two-dimensional complex torus T with
\Bbb Q (?d)\hookrightarrow End\Bbb Q (T){\Bbb Q }(\sqrt {d})\hookrightarrow {\rm{End_{{\Bbb Q }}}}(T) where
\Bbb Q (?d){\Bbb Q }(\sqrt {d}) is real quadratic, is algebraic. 相似文献
10.
R.J. McCann 《Geometric And Functional Analysis》2001,11(3):589-608
Let (M,g) be a connected compact manifold, C3 smooth and without boundary, equipped with a Riemannian distance d(x,y). If s : M ? M s : M \to M is merely Borel and never maps positive volume into zero volume, we show s = t °u s = t \circ u factors uniquely a.e. into the composition of a map t(x) = expx[-?y(x)] t(x) = {\rm exp}_x[-\nabla\psi(x)] and a volume-preserving map u : M ? M u : M \to M , where y: M ? \bold R \psi : M \to {\bold R} satisfies the additional property that (yc)c = y (\psi^c)^c = \psi with yc(y) :=inf{c(x,y) - y(x) | x ? M} \psi^c(y) :={\rm inf}\{c(x,y) - \psi(x)\,\vert\,x \in M\} and c(x,y) = d2(x,y)/2. Like the factorization it generalizes from Euclidean space, this non-linear decomposition can be linearized around the identity to yield the Hodge decomposition of vector fields.¶The results are obtained by solving a Riemannian version of the Monge--Kantorovich problem, which means minimizing the expected value of the cost c(x,y) for transporting one distribution f 3 0 f \ge 0 of mass in L1(M) onto another. Parallel results for other strictly convex cost functions c(x,y) 3 0 c(x,y) \ge 0 of the Riemannian distance on non-compact manifolds are briefly discussed. 相似文献
11.
In [C.K. Chui and X.L. Shi, Inequalities of Littlewood-Paley type for frames and wavelets, SIAM J. Math. Anal., 24 (1993), 263–277], the authors proved that if
{eimbxg(x-na): m,n ? \Bbb Z}\{e^{imbx}g(x-na): m,n\in{\Bbb Z}\}
is a Gabor frame for
L2(\Bbb R)L^2({\Bbb R})
with frame bounds A and B, then the following two inequalities hold:
A £ \frac2pb?n ? \Bbb Z|g(x-na)|2 £ B, a.e.A\le \frac{2\pi}{b}\sum_{n\in{\Bbb Z}}\vert g(x-na)\vert^2\le B, \quad a.e.
and
A £ \frac1a?m ? \Bbb Z|[^(g)](w-mb)|2 £ B, a.e.A\le \frac{1}{a}\sum_{m\in{\Bbb Z}}\vert \hat{g}(\omega-mb)\vert^2\le B, \quad a.e.
. In this paper, we show that similar inequalities hold for multi-generated irregular Gabor frames of the form
è1 £ k £ r{eiáx, l?gk(x-m): m ? Dk, l ? Lk }\bigcup_{1\le k\le r}\{e^{i\langle x, \lambda\rangle}g_{k}(x-\mu):\, \mu\in \Delta_k, \lambda\in\Lambda_k \}
, where Δ
k
and Λ
k
are arbitrary sequences of points in
\Bbb Rd{\Bbb R}^d
and
gk ? L2(\Bbb Rd)g_k\in{L^2{(\Bbb R}^d)}
, 1 ≤ k ≤ r. 相似文献
12.
K. W. Roggenkamp 《Archiv der Mathematik》2000,74(3):173-182
Let B\cal B be a p-block of cyclic defect of a Hecke order over the complete ring
\Bbb Z[q] áq-1,p ?\Bbb {Z}[q] _{\langle q-1,p \rangle}; i.e. modulo áq-1 ?\langle q-1 \rangle it is a p-block B of cyclic defect of the underlying Coxeter group G. Then B\cal B is a tree order over
\Bbb Z[q]áq-1, p ?\Bbb {Z}[q]_{\langle q-1, p \rangle } to the Brauer tree of B. Moreover, in case B\cal B is the principal block of the Hecke order of the symmetric group S(p) on p elements, then B\cal B can be described explicitly. In this case a complete set of non-isomorphic indecomposable Cohen-Macaulay B\cal B-modules is given. 相似文献
13.
B. Eckmann 《Archiv der Mathematik》2001,76(4):241-249
The complex group algebra \Bbb CG{\Bbb C}G of a countable group G can be imbedded in the von Neumann algebra NG of G. If G is torsion-free, and if P is a finitely generated projective module over \Bbb CG{\Bbb C}G it is proved that the central-valued trace of NG?\Bbb CGPNG\otimes _{{\Bbb C}G}P, i.e. of an idempotent \Bbb CG{\Bbb C}G-matrix A defining P is equal to the canonical trace k(P)\kappa (P) times identity I. It follows that k(P)\kappa (P) characterizes the isomorphism type of NG?\Bbb CGPNG\otimes _{{\Bbb C}G}P.¶If k(P)\kappa (P) is an integer, e.g., if the weak Bass conjecture holds for G then NG?\Bbb C GPNG\otimes _{{\Bbb C} G}P is free. It is also shown that for certain classes of groups geometric arguments can be used to prove the Bass conjecture. 相似文献
14.
V. Runde 《Archiv der Mathematik》2001,77(3):265-272
It is an open problem whether an infinite-dimensional amenable Banach algebra exists whose underlying Banach space is reflexive. We give sufficient conditions for a reflexive, amenable Banach algebra to be finite-dimensional (and thus a finite direct sum of full matrix algebras). If
\frak A {\frak A} is a reflexive, amenable Banach algebra such that for each maximal left ideal L of
\frak A {\frak A} (i) the quotient
\frak A/L {\frak A}/L has the approximation property and (ii) the canonical map from
\frak A \check? L^ {\frak A} \check{\otimes} L^\perp to
(\frak A / L) \check? L^ ({\frak A} / L) \check{\otimes} L^\perp is open, then
\frak A {\frak A} is finite-dimensional. As an application, we show that, if
\frak A {\frak A} is an amenable Banach algebra whose underlying Banach space is an
\scr Lp {\scr L}^p -space with p ? (1,¥) p\in (1,\infty) such that for each maximal left ideal L the quotient
\frak A/L {\frak A}/L has the approximation property, then
\frak A {\frak A} is finite-dimensional. 相似文献
15.
P. Biran 《Geometric And Functional Analysis》2001,11(3):407-464
We prove that every symplectic Kähler manifold (M;W) (M;\Omega) with integral [W] [\Omega] decomposes into a disjoint union (M,W) = (E,w0) \coprod D (M,\Omega) = (E,\omega_0) \coprod \Delta , where (E,w0) (E,\omega_0) is a disc bundle endowed with a standard symplectic form w0 \omega_0 and D \Delta is an isotropic CW-complex. We perform explicit computations of this decomposition on several examples.¶As an application we establish the following symplectic intersection phenomenon: There exist symplectically irremovable intersections between contractible domains and Lagrangian submanifolds. For example, we prove that every symplectic embedding j:B2n(l) ? \Bbb CPn \varphi:B^{2n}(\lambda) \to {\Bbb C}P^n of a ball of radius l2 3 1/2 \lambda^2 \ge 1/2 must intersect the standard Lagrangian real projective space \Bbb RPn ì \Bbb CPn {\Bbb R}P^n \subset {\Bbb C}P^n . 相似文献
16.
Friedrich Wehrung 《Algebra Universalis》1999,40(3):247-411
We introduce the dimension monoid of a lattice L, denoted by Dim L. The monoid Dim L is commutative and conical, the latter meaning that the sum of any two nonzero elements is nonzero. Furthermore, Dim L is given along with the dimension map, D\Delta from L2L to Dim L, which has the intuitive meaning of a distance function. The maximal semilattice quotient of Dim L is isomorphic to the semilattice Conc L of compact congruences of L; hence Dim L is a precursor of the congruence lattice of L. Here are some additional features of this construction: ¶¶ (1) Our dimension theory provides a generalization to all lattices of the von Neumann dimension theory of continuous geometries. In particular, if L is an irreducible continuous geometry, then Dim L is either isomorphic to \Bbb Z+\Bbb Z^+ or to \Bbb R+\Bbb R^+.¶ (2) If L has no infinite bounded chains, then Dim L embeds (as an ordered monoid) into a power of \Bbb Z+è{¥}.{\Bbb Z}^{+}\cup \{\infty\}.¶ (3) If L is modular or if L has no infinite bounded chains, then Dim L is a refinement monoid.¶ (4) If L is a simple geometric lattice, then Dim L is isomorphic to \Bbb Z+\Bbb Z^+, if L is modular, and to the two-element semilattice, otherwise.¶ (5) If L is an à0\aleph_0-meet-continuous complemented modular lattice, then both Dim L and the dimension function D\Delta satisfy (countable) completeness properties.¶¶ If R is a von Neumann regular ring and if L is the lattice of principal right ideals of the matrix ring M2 (R), then Dim L is isomorphic to the monoid V (R) of isomorphism classes of finitely generated projective right R-modules. Hence the dimension theory of lattices provides a wide lattice-theoretical generalization of nonstable K-theory of regular rings. 相似文献
17.
I. C. Michos 《Archiv der Mathematik》2000,75(3):188-194
Let Ln denote the n-th homogeneous component of the free Lie ring L(W) on a given \Bbb ZC2{{\Bbb Z}}C_{2}-lattice W. This paper gives explicit formulae for the multiplicities of the three indecomposable \Bbb ZC2{{\Bbb Z}}C_{2}-lattices in a Krull-Schmidt decomposition of Ln. In the case where W is a free \Bbb ZC2{{\Bbb Z}}C_{2}-lattice, Ln is shown to have no non-zero direct summand on which C2 acts trivially - this extends a result of R. M. Bryant for the special case where W is the regular \Bbb ZC2{{\Bbb Z}}C_{2}-lattice. As an application, the structure of the higher dimensional modules associated to a non-cyclic free presentation of C2 is determined. 相似文献
18.
Laura Abatangelo Alessandro Portaluri 《NoDEA : Nonlinear Differential Equations and Applications》2011,18(1):27-43
Given a Hilbert space (H,á·,·?){(\mathcal H,\langle\cdot,\cdot\rangle)}, and interval L ì (0,+¥){\Lambda\subset(0,+\infty)} and a map
K ? C2(H,\mathbb R){K\in C^2(\mathcal H,\mathbb R)} whose gradient is a compact mapping, we consider the family of functionals of the type:
I(l,u)=\dfrac12áu,u?-lK(u), (l,u) ? L×H.I(\lambda,u)=\dfrac12\langle u,u\rangle-\lambda K(u),\quad (\lambda,u)\in\Lambda\times\mathcal H. 相似文献
19.
The algebra Bp(\Bbb R){\cal B}_p({\Bbb R}), p ? (1,¥)\{2}p\in (1,\infty )\setminus \{2\}, consisting of all measurable sets in \Bbb R{\Bbb R} whose characteristic function is a Fourier p-multiplier, forms an algebra of sets containing many interesting and non-trivial elements (e.g. all intervals and their finite unions, certain periodic sets, arbitrary countable unions of dyadic intervals, etc.). However, Bp(\Bbb R){\cal B}_p({\Bbb R}) fails to be a s\sigma -algebra. It has been shown by V. Lebedev and A. Olevskii [4] that if E ? Bp(\Bbb R)E\in {\cal B}_p({\Bbb R}), then E must coincide a.e. with an open set, a remarkable topological constraint on E. In this note we show if $2 < p < \infty $2 < p < \infty , then there exists E ? Bp(\Bbb R)E\in {\cal B}_p({\Bbb R}) which is not in Bq(\Bbb R){\cal B}_q({\Bbb R}) for any q > pq>p. 相似文献
20.
Gerd Herzog 《Archiv der Mathematik》2001,77(3):215-221
Let f ? C(\Bbb Rn,\Bbb Rn) f\in C(\Bbb R^n,\Bbb R^n) be quasimonotone increasing such that Y(f(y)-f(x)) £ -c Y(y-x) (x << y) \Psi (f(y)-f(x)) \!\le -c \Psi (y-x) (x\ll y) for a linear and strictly positive functional Y \Psi and c > 0. We prove that f is a homeomorphism with decreasing and Lipschitz continuous inverse and we prove the global asymptotic stability of the equilibrium solution of x¢=f(x) x'=f(x) . 相似文献
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