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1.
Global existence and blow-up of solutions for a system of nonlinear viscoelastic wave equations with damping and source 总被引:1,自引:0,他引:1
In this paper we investigate the global existence and finite time blow-up of solutions to the system of nonlinear viscoelastic wave equations in Ω×(0,T) with initial and Dirichlet boundary conditions, where Ω is a bounded domain in . Under suitable assumptions on the functions gi(), , the initial data and the parameters in the equations, we establish several results concerning local existence, global existence, uniqueness and finite time blow-up property. 相似文献
2.
For any , let Pk denote the natural projections on ℓ1. Let |||||| be an equivalent norm of ℓ1 that satisfies all of the following four conditions:
- (1) There are α>4 and a positive (decreasing) sequence (αn) in (0,1) such that for any normalized block basis {fn} of (ℓ1,||||||) and xℓ1 with Pk−1(x)=x and |||x|||<αk,
- (2) There are two strictly decreasing sequences {βk} and {γk} withsuch that for any normalized block basis {fn} of (ℓ1,||||||) and x with (I−Pk)(x)=x,
- (3) For any , I−Pk=1.
- (4) The unit ball of (ℓ1,||||||) is σ(ℓ1,c0)-closed.
Keywords: Renorming; Fixed point property 相似文献
3.
Asymptotic behavior of solutions of nonlinear impulsive delay differential equations with positive and negative coefficients 总被引:1,自引:0,他引:1
This paper is concerned with the nonlinear impulsive delay differential equations with positive and negative coefficients (*) Sufficient conditions are obtained for every solution of equation (*) tending to a constant as t→∞. 相似文献
4.
We consider the eigenvalue problems for boundary value problems of second order difference equations(1) and(2) Comparison results for the eigenvalues of the problem (1) and the problem (2) are established. 相似文献
5.
Le Thi Phuong Ngoc Le Khanh Luan Tran Minh Thuyet Nguyen Thanh Long 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(11):5799-5819
In this paper, we consider the following nonlinear wave equation (1) where , , μ, f, g are given functions. To problem (1), we associate a linear recursive scheme for which the existence of a local and unique weak solution is proved by applying the Faedo–Galerkin method and the weak compact method. In the case of , , μ(z)≥μ0>0, μ1(z)≥0, for all , and , , , a weak solution uε1,ε2(x,t) having an asymptotic expansion of order N+1 in two small parameters ε1, ε2 is established for the following equation associated to (1)2,3: (2) 相似文献
6.
Let Γ denote a distance-regular graph with diameter D3. Let θ denote a nontrivial eigenvalue of Γ and let denote the corresponding dual eigenvalue sequence. In this paper we prove that Γ is Q-polynomial with respect to θ if and only if the following (i)–(iii) hold:
- (i) There exist such that
(1) - (ii) There exist such that the intersection numbers ai satisfyfor 0iD, where and are the scalars which satisfy Eq. (1) for i=0, i=D, respectively.
- (iii) for 1iD.
Keywords: Distance-regular graph; Q-polynomial; Association scheme 相似文献
7.
We introduce the family of linear operatorsassociated to a certain “admissible bunch” of operators St, t>0, acting on , and investigate the approximation properties of this family as α→0+. We give some applications to the Riesz and the Bessel potentials generated by the ordinary (Euclidean) and generalized translations. 相似文献
8.
Let , with
-1=x0n<x1n<<xnn<xn+1,n=1