共查询到20条相似文献,搜索用时 843 毫秒
1.
We study the asymptotic behaviour of the trajectories of the second order equation ${\ddot{x}(t)+\gamma \dot{x}(t)+\nabla\phi(x(t))+\varepsilon(t)x(t)=g(t)}We study the asymptotic behaviour of the trajectories of the second order equation [(x)\ddot](t)+g[(x)\dot](t)+?f(x(t))+e(t)x(t)=g(t){\ddot{x}(t)+\gamma \dot{x}(t)+\nabla\phi(x(t))+\varepsilon(t)x(t)=g(t)} , where γ > 0, g ? L1([0,+¥[;H){g \in L^1([0,+\infty[;H)}, Φ is a C
2 convex function and e{\varepsilon} is a positive nonincreasing function. 相似文献
2.
Stevan Pilipovi? Nenad Teofanov Joachim Toft 《Journal of Fourier Analysis and Applications》2011,17(3):374-407
Let ω,ω
0 be appropriate weight functions and q∈[1,∞]. We introduce the wave-front set, WFFLq(w)(f)\mathrm{WF}_{\mathcal{F}L^{q}_{(\omega)}}(f) of f ? S¢f\in \mathcal{S}' with respect to weighted Fourier Lebesgue space FLq(w)\mathcal{F}L^{q}_{(\omega )}. We prove that usual mapping properties for pseudo-differential operators Op (a) with symbols a in S(w0)r,0S^{(\omega _{0})}_{\rho ,0} hold for such wave-front sets. Especially we prove that
$[b]{lll}\mathrm{WF}_{\mathcal{F}L^q_{(\omega /\omega _0)}}(\operatorname {Op}(a)f)&\subseteq&\mathrm{WF}_{\mathcal{F}L^q_{(\omega )}}(f)\\[6pt]&\subseteq&\mathrm{WF}_{\mathcal{F}L^q_{(\omega/\omega _0)}}(\operatorname {Op}(a)f)\cup \operatorname {Char}(a).$\begin{array}[b]{lll}\mathrm{WF}_{\mathcal{F}L^q_{(\omega /\omega _0)}}(\operatorname {Op}(a)f)&\subseteq&\mathrm{WF}_{\mathcal{F}L^q_{(\omega )}}(f)\\[6pt]&\subseteq&\mathrm{WF}_{\mathcal{F}L^q_{(\omega/\omega _0)}}(\operatorname {Op}(a)f)\cup \operatorname {Char}(a).\end{array} 相似文献
3.
In this paper, we study the planar Hamiltonian system = J (A(θ)x + ▽f(x, θ)), θ = ω, x ∈ R2 , θ∈ Td , where f is real analytic in x and θ, A(θ) is a 2 × 2 real analytic symmetric matrix, J = (1-1 ) and ω is a Diophantine vector. Under the assumption that the unperturbed system = JA(θ)x, θ = ω is reducible and stable, we obtain a series of criteria for the stability and instability of the equilibrium of the perturbed system. 相似文献
4.
Nikolaos D. Atreas 《Advances in Computational Mathematics》2012,36(1):21-38
Let ϕ be a function in the Wiener amalgam space W¥(L1)\emph{W}_{\infty}(L_1) with a non-vanishing property in a neighborhood of the origin for its Fourier transform [^(f)]\widehat{\phi},
t={tn}n ? \mathbb Z{\bf \tau}=\{\tau_n\}_{n\in {{\mathbb Z}}} be a sampling set on ℝ and VftV_\phi^{\bf \tau} be a closed subspace of
L2(\mathbbR)L_2(\hbox{\ensuremath{\mathbb{R}}}) containing all linear combinations of τ-translates of ϕ. In this paper we prove that every function f ? Vftf\in V_\phi^{\bf \tau} is uniquely determined by and stably reconstructed from the sample set
Lft(f)={ò\mathbbR f(t)[`(f(t-tn))] dt}n ? \mathbb ZL_\phi^{\bf \tau}(f)=\Big\{\int_{\hbox{\ensuremath{\mathbb{R}}}} f(t) \overline{\phi(t-\tau_n)} dt\Big\}_{n\in {{\mathbb Z}}}. As our reconstruction formula involves evaluating the inverse of an infinite matrix we consider a partial reconstruction
formula suitable for numerical implementation. Under an additional assumption on the decay rate of ϕ we provide an estimate to the corresponding error. 相似文献
5.
Manfred Stoll 《Monatshefte für Mathematik》2005,141(5):131-139
Let B denote the unit ball in [(?)\tilde] \widetilde{\nabla\hskip-4pt}\hskip4pt
denote the volume measure and gradient with respect to the Bergman metric on B. In the paper we consider the weighted Dirichlet spaces
Dg{{\cal D}_{\gamma}}
,
$\gamma > (n-1)$\gamma > (n-1)
, and weighted Bergman spaces
Apa{A^p_{\alpha}}
,
0 < p < ¥0 < p < \infty
,
$\alpha > n$\alpha > n
, of holomorphic functions f on B for which
Dg( f)D_{\gamma}(\,f)
and
|| f||Apa\Vert\, f\Vert_{A^p_{\alpha}}
respectively are finite, where
Dg( f)=òB (1-|z|2)g|[(?)\tilde] f(z)|2dt(z),D_{\gamma}(\,f)=\int_B (1-\vert z\vert^2)^{\gamma}\vert\widetilde{\nabla\hskip-4pt}\hskip4pt f(z)\vert^2d\tau(z),
and
|| f||pApa=òB(1-|z|2)a| f(z)|pdt(z).\Vert\, f\Vert^p_{A^p_{\alpha}}=\int_B(1-\vert z\vert^2)^{\alpha}\vert\, f(z)\vert^pd\tau(z).
The main result of the paper is the following theorem.Theorem 1. Let f be holomorphic on B and
$\alpha > n$\alpha > n
. 相似文献
6.
Reinhard Farwig Christian Komo 《NoDEA : Nonlinear Differential Equations and Applications》2010,17(3):303-321
Let u be a weak solution of the Navier–Stokes equations in an exterior domain ${\Omega \subset \mathbb{R}^3}
7.
The aim of this study is to prove global existence of classical solutions for systems of the form ${\frac{\partial u}{\partial t} -a \Delta u=-f(u,v)}
8.
Julio Alcántara-Bode 《Integral Equations and Operator Theory》2005,53(3):301-309
It is proven that the set of eigenvectors and generalized eigenvectors associated to the non-zero eigenvalues of the Hilbert-Schmidt
(non nuclear, non normal) integral operator on L2(0, 1)
|