共查询到20条相似文献,搜索用时 250 毫秒
1.
For the Radon transform of functions with circular symmetry an inversion formula is proved in a new and elementary way. The inversion formula combined with Fourier theory is applied to Sommer-feld's integral for H, yielding a representation of products which generalizes Nicholson's integral for |H| 2. 相似文献
2.
We consider a domain Ω in ?n of the form Ω = ?l × Ω′ with bounded Ω′ ? ?n?l. In Ω we study the Dirichlet initial and boundary value problem for the equation ? u + [(? ? ?… ? ?)m + (? ? ?… ? ?)m]u = fe?iωt. We show that resonances can occur if 2m ≥ l. In particular, the amplitude of u may increase like tα (α rational, 0<α<1) or like in t as t∞∞. Furthermore, we prove that the limiting amplitude principle holds in the remaining cases. 相似文献
3.
Yang Zhijian 《Mathematical Methods in the Applied Sciences》2009,32(9):1082-1104
The paper studies the longtime behavior of solutions to the initial boundary value problem (IBVP) for a nonlinear wave equation arising in elasto‐plastic flow utt?div{|?u|m?1?u}?λΔut+Δ2u+g(u)=f(x). It proves that under rather mild conditions, the dynamical system associated with above‐mentioned IBVP possesses a global attractor, which is connected and has finite Hausdorff and fractal dimension in the phase spaces X1=H(Ω) × L2(Ω) and X=(H3(Ω)∩H(Ω)) × H(Ω), respectively. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
4.
Caisheng Chen Hui Wang ShengLan Zhu 《Mathematical Methods in the Applied Sciences》2011,34(5):497-508
In this work, we prove the existence of global attractor for the nonlinear evolution equation utt?Δu?Δut?Δutt + g(x, u)=f(x) in X=(H2(Ω)∩H(Ω)) × (H2(Ω)∩H(Ω)). This improves a previous result of Xie and Zhong in (J. Math. Anal. Appl. 2007; 336 :54–69.) concerning the existence of global attractor in H(Ω) × H(Ω) for a similar equation. Further, the asymptotic behavior and the decay property of global solution are discussed. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
5.
A. Kh. Khanmamedov 《Mathematical Methods in the Applied Sciences》2010,33(2):177-187
In this paper the long‐time behaviour of the solutions of 2‐D wave equation with a damping coefficient depending on the displacement is studied. It is shown that the semigroup generated by this equation possesses a global attractor in H(Ω) × L2(Ω) and H2(Ω)∩H(Ω) × H(Ω). Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
6.
Fernando Cobos Madrid 《Mathematische Nachrichten》1986,126(1):281-300
This article deals with the LORENTZ-MARCINKIEWICZ operator ideal ?? generated by an additive s-function and the LORENTZ-MARCINKIEWICZ sequence space λq(φ). We give eigenvalue distributions for operators belonging to ?? (E, E) and we show the interpolation properties of ??-ideals. Furthermore, we study certain SCHAUDER bases in ?? (H, K), H and K Hilbert spaces. 相似文献
7.
Jean-Pierre Lohac 《Mathematical Methods in the Applied Sciences》1991,14(3):155-175
Consider the advection–diffusion equation: u1 + aux1 ? vδu = 0 in ?n × ?+ with initial data u0; the Support of u0 is contained in ?(x1 < 0) and a: ?n → ? is positive. In order to approximate the full space solution by the solution of a problem in ? × ?+, we propose the artificial boundary condition: u1 + aux1 = 0 on ∑. We study this by means of a transmission problem: the error is an O(v2) for small values of the viscosity v. 相似文献
8.
Thomas Schott 《Mathematische Nachrichten》1998,196(1):231-250
This paper is a continuation of [8]. We study weighted function spaces of type B and F on the Euclidean space Rn, where u is a weight function of at most exponential growth. In particular, u(χ (±|χ|) is an admissible weight. We deal with atomic decompositions of these spaces. Furthermore, we prove that the spaces B and F are isomorphic to the corresponding unweighted spaces B and F. 相似文献
9.
We prove stability of the kink solution of the Cahn‐Hilliard equation ∂tu = ∂( ∂u − u/2 + u3/2), x ∈ ℝ. The proof is based on an inductive renormalization group method, and we obtain detailed asymptotics of the solution as t → ∞. We prove stability of the kink solution of the Cahn‐Hilliard equation ∂tu = ∂( ∂u − u/2 + u3/2), x ∈ ℝ. The proof is based on an inductive renormalization group method, and we obtain detailed asymptotics of the solution as t → ∞. © 1999 John Wiley & Sons, Inc. 相似文献
10.
In this paper, some sufficient conditions under which the quasilinear elliptic system ‐div(∣?u∣p‐2?u) = uv, ‐div(∣?u∣q‐2?u) = uv in ?N(N≥3) has no radially symmetric positive solution is derived. Then by using this non‐existence result, blow‐up estimates for a class of quasilinear reaction–diffusion systems ut = div (∣?u∣p‐2?u)+uv,vt = div(∣?v∣q‐2?v) +uv with the homogeneous Dirichlet boundary value conditions are obtained. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
11.
For graphs A, B, let () denote the number of subsets of nodes of A for which the induced subgraph is B. If G and H both have girth > k, and if () = () for every k-node tree T, then for every k-node forest F, () = (). Say the spread of a tree is the number of nodes in a longest path. If G is regular of degree d, on n nodes, with girth > k, and if F is a forest of total spread ≤k, then the value of () depends only on n and d. 相似文献
12.
Nicola Visciglia 《Mathematical Methods in the Applied Sciences》2004,27(18):2153-2170
We consider the following semilinear wave equation: (1) for (t,x) ∈ ?t × ?. We prove that if the potential V(t,x) is a measurable function that satisfies the following decay assumption: ∣V(t,x)∣?C(1+t)(1+∣x∣) for a.e. (t,x) ∈ ?t × ? where C, σ0>0 are real constants, then for any real number λ that satisfies there exists a real number ρ(f,g,λ)>0 such that the equation has a global solution provided that 0<ρ?ρ(f,g,λ). Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
13.
This paper is the continuation of [17]. We investigate mapping and spectral properties of pseudodifferential operators of type Ψ with χ χ ? ? and 0 ≤ γ ≤ 1 in the weighted function spaces B (?n, w(x)) and F (?n, w(x)) treated in [17]. Furthermore, we study the distribution of eigenvalues and the behaviour of corresponding root spaces for degenerate pseudodifferential operators preferably of type b2(x) b(x, D) b1(x), where b1(x) and b2(x) are appropriate functions and b(x, D) ? Ψ. Finally, on the basis of the Birman-Schwinger principle, we deal with the “negative spectrum” (bound states) of related symmetric operators in L2. 相似文献
14.
Nakao Hayashi Masahiro Ikeda Pavel I. Naumkin 《Mathematical Methods in the Applied Sciences》2011,34(8):896-910
We prove the existence of the wave operator for the system of the massive Dirac–Klein–Gordon equations in three space dimensions x∈ R 3 where the masses m, M>0. We prove that for the small final data , (?, ?)∈ H 2 + µ, 1 × H 1 + µ, 1, with and , there exists a unique global solution for system (1) with the final state conditions Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
15.
Olaf Bhme 《Mathematische Nachrichten》1983,113(1):163-169
By using the LITTLEWOOD matrices A2n we generalize CLARKSON' S inequalities, or equivalently, we determine the norms ‖A2n: l(LP) → l(LP)‖ completely. The result is compared with the norms ‖A2n: l → l‖, which are calculated implicitly in PIETSCH [6]. 相似文献
16.
Matthias Winter 《Mathematical Methods in the Applied Sciences》1995,18(2):147-168
We consider the equation (?1)m?m (p?mu) + ?u = ? in ?n × (0, ∞) for arbitrary positive integers m and n and under the assumptions p ? 1, ? ? C(?n) and p > 0. Even if the differential operator (?1)m?m (p?mu) has no eigenvalues, the solution u(x,t) may increase as t → ∞ for 2m ≥ n. For this case, we derive necessary and sufficient conditions for the convergence of u(x,t) as t → ∞. Furthermore, we characterize the functions occurring in these conditions as solutions of the homogeneous static equation (?1)m?m (p?mu) = 0, which satisfy appropriate asymptotic conditions at infinity. We also give an asymptotic characterization of the static limit. 相似文献
17.
Matthias Winter 《Mathematical Methods in the Applied Sciences》1995,18(1):1-25
We consider the equation (?1)m?m (p?mu) + ?u = ? in ?n × [0, ∞] for arbitrary positive integers m and n and under the assumptions p ?1, ? ? C and p > 0. Under the additional assumption that the differential operator (?1)m?m (p?mu) has no eigenvalues we derive an asymptotic expansion for u(x,t) as t → including all terms up to order o(1). In particular, we show that for 2m ≥ n terms of the orders tα, log t, (log t)2 and tβ·log t as t → ∞ may occur. 相似文献
18.
We study the maximal function Mf(x) = sup |f(x + y, t)| when Ω is a region in the (y,t) Ω upper half space R and f(x, t) is the harmonic extension to R+N+1 of a distribution in the Besov space Bαp,q(RN) or in the Triebel-Lizorkin space Fαp,q(RN). In particular, we prove that when Ω= {|y|N/ (N-αp) < t < 1} the operator M is bounded from F (RN) into Lp (RN). The admissible regions for the spaces B (RN) with p < q are more complicated. 相似文献
19.
Roman Murawski 《Mathematical Logic Quarterly》1992,38(1):59-84
We consider iterations of satisfaction classes and apply them to construct expansions of models of Peano arithmetic to models of A|Δ+∑-AC. 1991 MSC: 03F35, 03C62. 相似文献
20.
John F. P. Hudson 《Journal of Graph Theory》1999,32(3):298-302
Lins has conjectured that the two 3-manifolds that he refers to as H and H̄ are not homeomorphic. He suggests that their fundamental groups may be the same, but that they may be distinguishable by their quantum invariants. This article describes the proof that they, in fact, have different fundamental groups. © 1999 John Wiley & Sons, Inc. J Graph Theory 32: 298–302, 1999 相似文献