Global solutions for quasilinear parabolic problems

Results on the global existence of classical solutions for quasilinear parabolic equations in bounded domains with homogeneous Dirichlet or Neumann boundary conditions are presented. Besides quasilinear parabolic equations, the method is also applicable to some weakly-coupled reaction-diffusion systems and to elliptic equations with nonlinear dynamic boundary conditions. Received December 21, 2000; accepted August 30, 2001.     

Periodic Solutions of a Nonlinear Evolution Problem

In this paper we prove existence of periodic solutions to a nonlinear evolution system of second order partial differential equations involving the pseudo-Laplacian operator. To show the existence of periodic solutions we use Faedo-Galerkin method with a Schauder fixed point argument.     

PEGylation of chitosan for improved solubility and fiber formation via electrospinning

PEG-N-chitosan and PEG-N,O-chitosan were synthesized via reductive amination and acylation of chitosan, respectively. The structures were confirmed by FTIR and H¹NMR. The extents of PEGylation increased with reducing chain lengths of either chitosan (M _v = 137–400 kDa) or poly(ethyelene glycol) (PEG, M _n = 500–2 kDa). Water solubility were easily achieved at degree of substitution (DS) as low as 0.2 for either derivtive whereas the PEG-N,O-chitosan at DS = 1.5 was soluble in organic solvents, including CHCl₃, DMF, DMSO and THF. None of the aqueous solutions of PEG-N-chitosan or PEG-N,O-chitosan alone could be electrospun into fibers. Electrospinning of PEG550-N,O-chitosan145 at 25% in DMF produced fibrous structure intermixed with beads. The efficiency of fiber formation and the uniformity of fibers were improved by increasing the solution viscosity using a cosolvent or reducing the solution surface tensions with a non-ionic surfactant. Ultra-fine fibers with diameters ranging from 40 nm to 360 nm and an average diameter of 162 nm were efficiently generated from electrospinning of 15% PEG550-N,O-chitosan145 in 75/25 (v/v) THF/DMF cosolvents with 0.5% Triton X-100^TM.     

具有吸收-反射边界的Boltzmann-Poisson输运模型的整体弱解

本文研究具有吸收-反射边界的Boltzmann-Poisson输运模型的初这值问题,并利用速度平均的稳定性和L~1空间紧致性理论,在较弱的初边值条件下,证明了其整体弱解的存在性。     

考虑量子效应的Zakharov方程组的孤波解

借助Maple程序，利用扩展的双曲函数法和双函数法求解了考虑量子效应的Zakharov方程组，得到了多种孤波解，其中包括亮孤波解、W型孤波解、M型孤波解和奇性孤波解. 关键词： 量子效应 Zakharov方程组 扩展的双曲函数法 孤波解     

GLOBAL EXISTENCE FOR SEMILINEAR RETARDED FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAY

This paper is concerned with the global existence of solutions for abstract retarded functional differential equations (RFDEs) with infinite delay,via a fixed point approach.Some sufficient conditions are established under which the existence of a globally mild solution are obtained by using Leray-Schauder.     

非线性二阶中立型时滞微分方程正解的存在性

考虑非线性二阶中立型微分方程,[a(t)x(t)-∑ from i=1 to m (p_i(t)x(τi(t)))]″-∫from n=a to b (f(t,ξ,x[g(t,ξ)])dσ(ξ))=0,t≥t_0,和相应不等式[a(t)x(t)-∑ from i=1 to m (p_i(t)x(τi(t)))]″-∫from n=a to b (f(t,ξ,x[g(t,ξ)])dσ(ξ))≥0,t≥t_0.存在正解是相互等价的.其中a(t),pi(t)∈C([t0,∞),R+),a(t)>0,τi(t)∈C(R~+,R~+),τi(t)t,limt→∞τi(t)=∞(i=1,2,…,m).g(t,ξ)∈C([t_0,∞)×[a,b],R+).g(t,ξ)是分别关于t和ξ的增函数.g(t,ξ)t,ξ∈[a,b],limt→∞,ξ∈[a,b]g(t,ξ)=∞.f(t,ξ,x)∈C([t_0,∞)×[a,b]×R,R+).当x>0时,xf(t,ξ,x)>0.σ(ξ)∈C([a,b],R),且σ(ξ)非减.     

A Connection between Singular Stochastic Control and Optimal Stopping

We show that the value function of a singular stochastic control problem is equal to the integral of the value function of an associated optimal stopping problem. The connection is proved for a general class of diffusions using the method of viscosity solutions.     

Nonlinear Double-well Schrödinger Equations in the Semiclassical Limit

We consider time-dependent Schrödinger equations with a double well potential and an external nonlinear, both local and non-local, perturbation. In the semiclassical limit, the finite dimensional eigenspace associated to the lowest eigenvalues of the linear operator is almost invariant for times of the order of the beating period and the dominant term of the wavefunction is given by means of the solutions of a finite dimensional dynamical system. In the case of local nonlinear perturbation, we assume the spatial dimension d=1 or d=2.     

Solvent‐Polymeric ISEs Tailored for Measurements in Solutions Containing Tetrabutylammonium,Cesium, and Calcium Ions

Ion‐selective electrodes are described, with membranes tailored for measurements of tetrabutylammonium ions in aqueous and formamide solutions, and for measurements of cesium and calcium ions in the presence of tetrabutylammonium. It is shown that reliable measurements of cesium ions are possible when a correction is introduced for interference from tetrabutylammonium, using Nikolsky selectivity coefficient. A novel membrane composition is described which ensures high selectivity to calcium ions over tetrabutylammonium.