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1.
We consider the numerical discretization of singularly perturbed Volterra integro-differential equations (VIDE) (*) and Volterra integral equations (VIE) (**) by tension spline collocation methods in certain tension spline spaces, where is a small parameter satisfying 0<1, and q1, q2, g and K are functions sufficiently smooth on their domains to ensure that Eqs. (*) and (**) posses a unique solution.We give an analysis of the global convergence properties of a new tension spline collocation solution for 0<1 for singularly perturbed VIDE and VIE; thus, extending the existing theory for =1 to the singularly perturbed case. 相似文献
2.
We study the Hindmarsh–Rose burster which can be described by the differential system = y-x~3+ bx~2+ I-z, = 1-5 x2~-y, z = μ(s(x-x_0)-z),where b, I, μ, s, x_0 are parameters. We characterize all its invariant algebraic surfaces and all its exponential factors for all values of the parameters. We also characterize its Darboux integrability in function of the parameters. These characterizations allow to study the global dynamics of the system when such invariant algebraic surfaces exist. 相似文献
3.
Let B denote the unit ball of . For 0<p<∞, the holomorphic function spaces Qp and Qp,0 on the unit ball of are defined as and In this paper, we give some derivative-free, mixture and oscillation characterizations for Qp and Qp,0 spaces in the unit ball of . 相似文献
4.
Blow-up analysis for a system of heat equations with nonlinear flux which obey different laws 总被引:1,自引:0,他引:1
We consider a system of heat equations ut=Δu and vt=Δv in Ω×(0,T) completely coupled by nonlinear boundary conditions We prove that the solutions always blow up in finite time for non-zero and non-negative initial values. Also, the blow-up only occurs on ∂Ω with for p,q>0, 0≤α<1 and 0≤β<p. 相似文献
5.
Fordyce A. Davidson Bryan P. Rynne 《Journal of Mathematical Analysis and Applications》2004,300(2):491-504
Let TR be a time-scale, with a=infT, b=supT. We consider the nonlinear boundary value problem (2) (4)
u(a)=u(b)=0,