LARGE-TIME BEHAVIOR OF SOLUTIONS OF QUANTUM HYDRODYNAMIC MODEL FOR SEMICONDUCTORS

A one-dimensional quantum hydrodynamic model （or quantum Euler-Poisson system） for semiconductors with initial boundary conditions is considered for general pressure-density function. The existence and uniqueness of the classical solution of the corresponding steady-state quantum hydrodynamic equations is proved. Furthermore, the global existence of classical solution, when the initial datum is a perturbation of t he steadystate solution, is obtained. This solution tends to the corresponding steady-state solution exponentially fast as the time tends to infinity.

Large-time Behavior of Solutions to the Stokes Approximation Equations for Two Dimensional Compressible Flows

In this paper, we study the large time asymptotic behavior of solutions to both the Cauchy problem and the exterior problem of the Stokes approximation equations of two dimensional compressible flows.

High-Order Soliton Solutions and Hybrid Behavior for the (2 + 1)-Dimensional Konopelchenko-Dubrovsky Equations

In this paper, the evolutionary behavior of N-solitons for a (2 + 1)-dimensional Konopelchenko-Dubrovsky equations is studied by using the Hirota bilinear method and the long wave limit method. Based on the N-soliton solution, we first study the evolution from N-soliton to T-order (T=1,2) breather wave solutions via the paired-complexification of parameters, and then we get the N-order rational solutions, M-order (M=1,2) lump solutions, and the hybrid behavior between a variety of different types of solitons combined with the parameter limit technique and the paired-complexification of parameters. Meanwhile, we also provide a large number of three-dimensional figures in order to better show the degeneration of the N-soliton and the interaction behavior between different N-solitons.

Asymptotic Behavior and Nonexistence of Positive Solutions of Delay Difference Equations *L

Aim To obtain new criteria for asymptotic behavior and nonexistence of positive solutions of nonlinear neutral delay difference equations. Methods By means of Hlder inequality and a method of direct analysis, some interesting Lemmas were offered. Results and Conclusion New criteria for asymptotic behavior and nonexistence of positive solutions of nonlinear neutral delay difference equations are established, which extend and improve the results obtained in the literature. Some interesting examples illustrating the importance of our results are also included.

NORMALIZED SOLUTIONS FOR THE GENERAL KIRCHHOFF TYPE EQUATIONS

In the present paper,we prove the existence,non-existence and multiplicity of positive normalized solutions(λ_(c),u_(c))∈R×H^(1)(R^(N))to the general Kirchhoff problem-M■,satisfying the normalization constraint f_(R)^N u^2dx=c,where M∈C([0,∞))is a given function satisfying some suitable assumptions.Our argument is not by the classical variational method,but by a global branch approach developed by Jeanjean et al.[J Math Pures Appl,2024,183:44–75]and a direct correspondence,so we can handle in a unified way the nonlinearities g(s),which are either mass subcritical,mass critical or mass supercritical.

Adsorption behaviors and mechanisms of gold recovery from thiosulfate solution by ion exchange resin

The adsorption behaviors and mechanisms of gold from thiosulfate solution on strong-base anion exchange resin were systematically investigated.The comparison experiment of adsorption ability and selectivity for gold showed that gel Amberlite IRA-400 resin with Type Ⅰ quaternary ammonium functional group had better adsorption performance.The increases of resin dosage,ammonia concentration and solution pH were favorable to gold adsorption,whereas the rises of cupric and thiosulfate concentrations were disadvantageous to gold loading.Microscopic characterization results indicated that gold was adsorbed in the form of [Au(S_(2)O_(3))_(2)]^(3–) complex anion by exchanging with the counter ion Cl^(–) in the functional group of the resin.Density functional theory calculation result manifested that gold adsorption was mainly depended on the hydrogen bond and van der Waals force generated between O atom in [Au(S_(2)O_(3))_(2)]^(3–) and H atom in the quaternary ammonium functional group of the resin.

LIMITING BEHAVIOR OF BLOW-UP SOLUTIONS OF THE NLSE WITH A STARK POTENTIAL

This article is concerned with blow-up solutions of the Cauchy problem of critical nonlinear SchrSdinger equation with a Stark potential. By using the variational characterization of corresponding ground state, the limiting behavior of blow-up solutions with critical and small super-critical mass are obtained in the natural energy space ∑ = {u ∈ H^1; fRN ｜x｜^2｜u｜^2dx 〈 ＋∞）}. Moreover, an interesting concentration property of the blow-up solutions with critical mass is gotten, which reads that ｜u（t, x）｜^2→ ｜｜Q｜｜L^2 2 δx=x1 as t → T.

Electrospinning and Rheological Behavior of Poly(vinyl alcohol)/Collagen Blended Solutions

Poly（vinyl alcohol）/collagen （PVA/COL） micro-nanofibers were successfully prepared by electrospinning process. Water, green, and non-toxic was used as the solvent. The electrospun mats consisted of micro-nanoscale fibers with mean diameter ranging from approximately 363 nm to 179 nm. It was observed that the mean diameters of PVA/COL electrospun fibers decreased with increasing collagen content. The effects of PVA/COL blending ratio on the rheological behavior of PVA/COL blended solutions were investigated by rotate rheometer. It was found that PVA/COL blended solutions behaved as Non-Newtonian fluids. With increasing collagen content, the Non-Newtonian index （n） of PVA/COL blended solutions decreased. Meanwhile, a linear relationship was found between the Non-Newtonian index （n） and the mean diameters of the PVA/COL micro- nanofibers. The chemical structures of PVA/COL electrospun fibers were also characterized by FTIR.

EXISTENCE AND ASYMPTOTIC BEHAVIOR OF THE SOLUTIONS FOR A NONLINEAR ELLIPTIC EQUATION ARISING IN ASTROPHYSICS

The author first analyzes the existence of ground state solutions and cylindrically symmetric solutions and then the asymptotic behavior of the ground state solution of the equation -△u =φ（r）u^p-1, u 〉 0 in R^N, u ∈ D^1,2（R^N）, where N ≥ 3, x = （x^1,z） ∈ R^K×R^N-K,2 ≤ K ≤ N,r = ｜x′｜. It is proved that for 2（N-s）/（N-2） 〈 p 〈 2^＊ = 2N/（N - 2）, 0 〈 s 〈 2, the above equation has a ground state solution and a cylindrically symmetric solution. For p = 2^＊, the above equation does not have a ground state solution but a cylindrically symmetric.solution, and when p close to 2^＊, the ground state solutions are not cylindrically symmetric. On the other hand, it is proved that as p close to 2＊, the ground state solution Up has a unique maximum point xp = （x′p, Zp） and as p → 2^＊, ｜x′p｜ → r0 which attains the maximum of φ on R^N. The asymptotic behavior of ground state solution Up is also given, which also deduces that the ground state solution is not cylindrically symmetric as p goes to 2^＊.

ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO THE HEAT EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS

The purpose of this paper is to investigate the stability and asymptotic behavior of the time-dependent solutions to a linear parabolic equation with nonlinear boundary condition in relation to their corresponding steady state solutions. Then, the above results are extended to a semilinear parabolic equation with nonlinear boundary condition by analyzing the corresponding eigenvalue problem and using the method of upper and lower solutions.

Rheological Behavior for Polymer Melts and Concentrated Solutions——Part Ⅶ: A Quantitative Verification for the Molecular Theory of Non-linear Viscoelasticity with Entanglement Constraints in Polymer Melts

Based on the molecular theory of non-linear viscoelasticity with constrained entanglements in polymer melts, the material functions in simple shear flow were formulated, the theoretical relations between. eta((gamma) over dot), psi (10)((gamma) over dot) and shear rate ((gamma) over dot), and topologically constrained dimension number n ' and a were derived. Linear viscoelastic parameters (eta (0) and G(N)(0)) and topologically constrained dimension number (n ' a and <(<upsilon>)over bar>) as a function of the primary molecular weight (M-n), molecular weight between entanglements (M-C) and the entanglement sites sequence distribution in polymer chain were determined. A new method for determination of viscoelastic parameters (eta (0), psi (10), G(N)(0) and J(e)(0)), topologically constrained dimension number (n ', a and v) and molecular weight (M-n, M-c and M-e) from the shear flow measurements was proposed. It was used to determine those parameters and structures of HDPE, making a good agreement between these values and those obtained by other methods. The agreement affords a quantitative verification for the molecular theory of nonlinear viscoelasticity with constrained entanglement in polymer melts.

Corrosion behavior of CuCrNiAl alloy in HCl solutions

The corrosion behavior of a CuCrNiAl alloy in HCl solutions was studied by means of metallograph, XRD, SEM/EDX and TEM methods. The results show that in low concentration of HCl solutions, Cu of CuCrNiAl alloy is more easily subject to corrsion than Cr; the dechromisation of the CuCrNiAl alloy occurs at a certain concentration of HCl solutions, at the same time Al of CuCrNiAl alloy is subject to corrosion also. The dechromisation corrosion occurs initially at the interface between Cr phase and Cu phase, then it gradually extends Cr phase until Cr phase is dissolved completely. It is also revealed that the tendency of dechromisaion of the CuCrNiAl alloy increases with the increase in concentration and temperature of HCl solutions.

ASYMPTOTIC BEHAVIOR OF GLOBAL SMOOTH SOLUTIONS FOR BIPOLAR COMPRESSIBLE NAVIER-STOKES-MAXWELL SYSTEM FROM PLASMAS

This paper is concerned with the bipolar compressible Navier-Stokes-Maxwell system for plasmas. We investigated, by means of the techniques of symmetrizer and elaborate energy method, the Cauchy problem in R^3. Under the assumption that the initial values are close to a equilibrium solutions, we prove that the smooth solutions of this problem converge to a steady state as the time goes to the infinity. It is shown that the difference of densities of two carriers converge to the equilibrium states with the norm ｜｜·｜｜H^s-1, while the velocities and the electromagnetic fields converge to the equilibrium states with weaker norms than ｜｜·｜｜H^s-1. This phenomenon on the charge transport shows the essential difference between the unipolar Navier-Stokes-Maxwell and the bipolar Navier-Stokes-Maxwell system.

Corrosion-wear behavior of nanocrystalline Fe88Si12 alloy in acid and alkaline solutions

The corrosion-wear behavior of a nanocrystalline Fe_（88）Si_（12） alloy disc coupled with a Si_3N_4 ball was investigated in acid（pH 3） and alkaline（pH 9） aqueous solutions. The dry wear was also measured for reference. The average friction coefficient of Fe_（88）Si_（12） alloy in the pH 9 solution was approximately 0.2, which was lower than those observed for Fe_（88）Si_（12） alloy in the pH 3 solution and in the case of dry wear. The fluctuation of the friction coefficient of samples subjected to the pH 9 solution also showed similar characteristics. The wear rate in the pH 9 solution slightly increased with increasing applied load. The wear rate was approximately one order of magnitude less than that in the pH 3 solution and was far lower than that in the case of dry wear, especially at high applied load. The wear traces of Fe_（88）Si_（12） alloy under different wear conditions were examined and analyzed by scanning electron microscopy, energy-dispersive X-ray spectroscopy, and X-ray photoelectron spectroscopy. The results indicated that the tribo-chemical reactions that involve oxidation of the worn surface and hydrolysis of the Si_3N_4 ball in the acid solution were restricted in the pH 9 aqueous solution. Thus, water lubrication can effectively improve the wear resistance of nanocrystalline Fe_（88）Si_（12） alloy in the pH 9 aqueous solution.

In situ backscattered electron imaging study of the effect of annealing on the deformation behaviors of Ni electroformed from additive-free and saccharin-containing sulfamate solutions

The Ni samples were electroformed from additive-free(AF) and saccharin-containing(SC) sulfamate solutions, respectively. In situ backscattered electron(BSE) imaging, electron backscatter diffraction(EBSD), and electron-probe microanalysis(EPMA) were used to investigate the effect of annealing on the deformation behaviors of the AF and SC samples. The results indicate that columnar grains of the as-deposited AF sample had an approximated average width of 3 μm and an approximated aspect ratio of 8. The average width of columnar grains of the as-deposited SC sample was reduced to approximately 400 nm by the addition of saccharin to the electrolyte. A few very-large grains distributed in the matrix of the SC sample after annealing. No direct evidence indicated that S segregated at the grain boundaries before or after annealing. The average value of the total elongations of the SC samples decreased from 16% to 6% after annealing, whereas that of the AF samples increased from 18% to 50%. The dislocation recovery in grain-boundary areas of the annealed AF sample was reduced, which contributed to the appearance of microvoids at the triple junctions. The incompatibility deformation between very-large grains and fine grains contributed to the brittle fracture behavior of the annealed SC Ni.

Asymptotic Behavior of the Solutions to the One-Dimensional Nonisentropic Hydrodynamic Model for Semiconductors

In this paper, the asymptotic behavior of the global smooth solutions to the Cauchy problem for the one-dimensional nonisentropic Euler-Poisson （or full hydrodynamic） model for semiconductors, where the energy equation with non-zero thermal conductivity coefficient are contained, is discussed. The global existence of smooth solutions for the Cauchy problem with small perturbed initial data is proved. In particular, that the solutions converge to the corresponding stationary solutions exponentially fast as t → ∞ is showed.

Dynamical behaviors of traveling wave solutions to a Fujimoto-Watanabe equation

We study dynamical behaviors of traveling wave solutions to a Fujimoto-Watanabe equation using the method of dynamical systems. We obtain all possible bifurcations of phase portraits of the system in different regions of the threedimensional parameter space. Then we show the required conditions to guarantee the existence of traveling wave solutions including solitary wave solutions, periodic wave solutions, kink-like（antikink-like） wave solutions, and compactons. Moreover, we present exact expressions and simulations of these traveling wave solutions. The dynamical behaviors of these new traveling wave solutions will greatly enrich the previews results and further help us understand the physical structures and analyze the propagation of nonlinear waves.

On the Behavior of the Positive Solutions of the System of Two Higher-Order Rational Difference Equations

We study the convergence of the positive solutions of the system of the following two difference equations: where K is a positive integer, the parameters?A,B,?α, β? and the initial conditions are positive real numbers. Our results generalize well known results in [1,2].

LONG-TIME BEHAVIOR OF TRANSIENT SOLUTIONS FOR CELLULAR NEURAL NETWORK SYSTEMS

By establishing concept an transient solutions of general nonlinear systems converging to its equilibrium set, long-time behavior of solutions for cellular neural network systems is studied. A stability condition in generalized sense is obtained. This result reported has an important guide to concrete neural network designs.

ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR THE CHAFEE-INFANTE EQUATION

In higher dimension,there are many interesting and challenging problems about the dynamics of non-autonomous Chafee-Infante equation.This article is concerned with the asymptotic behavior of solutions for the non-autonomous Chafee-Infante equation∂u∂t−Δu=λ(t)(u−u3)in higher dimension,whereλ(t)∈C1[0,T]andλ(t)is a positive,periodic function.We denoteλ1 as the first eigenvalue of−Δφ=λφ,x∈Ω;φ=0,x∈∂Ω.For any spatial dimension N≥1,we prove that ifλ(t)≤λ1,then the nontrivial solutions converge to zero,namely,limt→+∞u(x,t)=0,x∈Ω;ifλ(t)>λ1 as t→+∞,then the positive solutions are"attracted"by positive periodic solutions.Specially,ifλ(t)is independent of t,then the positive solutions converge to positive solutions of−ΔU=λ(U−U^3).Furthermore,numerical simulations are presented to verify our results.