EXISTENCE AND UNIQUENESS OF THE SOLUTION FOR NONLINEAR THIRD-ORDER ROBIN BOUNDARY VALUE PROBLEM WITH A TURNING POINT

The paper aims to obtain existence and uniqueness of the solution as well as asymptotic estimate of the solution for singularly perturbed nonlinear third- order Robin boundary value problem with a turning point.In order to achieve this aim,existence and uniqueness of the solution for third-order nonlinear Robin boundary value problem is derived first based on the upper and lower solutions method under relatively weaker conditions.In this manner,the goal of this paper is gained by applying the existence and uniqueness results mentioned above.     

Hele-Shaw type problems with dynamical boundary conditions

In this paper, we study the nonlinear evolution equation of Hele-Shaw type with dynamical boundary conditions. That is, the equation ut=Δw+f where u∈H(w) and H is the Heaviside function, with boundary condition μ(x,w)t_∂w+k∇w⋅ν=g, where ν denotes the outward normal vector of the fixed boundary of the domain. We prove existence, uniqueness and some qualitative properties of the solution.     

Variational conclusions of set-valued bifunctions on convex subsets of Banach spaces with applications

In this paper, variational conclusions of set-valued bifunctions on convex subsets of Banach spaces are investigated and several new results are obtained. The results are applied to the fixed point theory and variational inequalities. We obtain two fixed point theorems and existence theorems of solutions of variational inequalities.     

关于《一类奇异边值问题的正解》的注记

文[4]通过构造反例断言文[1]中定理的必要性证明有误,本文首先指出文[4] 的这个断言不正确,然后对文[4]中定理2.1作了本质性的改进.     

Physicochemical studies on hydrophobic PEO‐PPO‐PEO triblock copolymer micelles in SDS micellar environment

The shape, size, aggregation, hydration, and correlation times of water insoluble PEO‐PPO‐PEO triblock copolymer micelles with sodium dodecylsulfate (SDS) micelles were investigated using transport studies and dynamic light scattering technique. From the conductance of micellar solutions of the polymer in 25 mM SDS and 5 mM NaCl, the hydration of polymer micelles were determined using the principle of obstruction of electrolyte migration by the polymer. The asymmetry of the micellar particles of polymer and polymer‐SDS mixed micellar systems in 5 mM NaCl and their average axial ratios were calculated using intrinsic viscosity and hydration data obeying Simha–Einstein equation. Hydration number and micellar sizes were variable with temperature. The shape of the polymer micelles has been ellipsoidal rather than spherical. The micellar volume, hydrodynamic radius, radius of gyration, diffusional coefficients as well as translational, rotational and effective correlation times have been calculated from the absolute values of the axes. The partial molal volume of polymer micelles has also been determined and its comparison with the molar volume of pure polymer suggested a volume contraction due to immobilization of the water phase by the hydrophilic head groups of the polymer. The thermodynamic activation parameters for viscous flow favor a more ordered water structure around polymer micelles at higher temperatures. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 2410–2420, 2007     

Theory of Valuations on Manifolds: A Survey

This is a non-technical survey of a recent theory of valuations on manifolds constructed in [A10], [A11], [AF] and [A12], and actually a guide to this series of articles. We also review some recent related results obtained by a number of people. Received: February 2006, Revision: June 2006, Accepted: June 2006     

A Nonlinear Drift - Diffusion System with Electric Convection Arising in Electrophoretic and Semiconductor Modeling

A multi-dimensional transient drift-diffusion model for (at most) three charged particles, consisting of the continuity equations for the concentrations of the species and the Poisson equation for the electric potential, is considered. The diffusion terms depend on the concentrations. Such a system arises in electrophoretic modeling of three species (neutrally, positively and negatively charged) and in semiconductor theory for two species (positively charged holes and negatively charged electrons). Diffusion terms of degenerate type are also possible in semiconductor modeling. For the initial boundary value problem with mixed Dirichlet - Neumann boundary conditions and general reaction rates, a global existence result is proved. Uniqueness of solutions follows in the Dirichlet boundary case if the diffusion terms are uniformly parabolic or if the initial and boundary densities are strictly positive. Finally, we prove that solutions exist which are positive uniformly in time and globally bounded if the reaction rates satisfy appropriate growth conditions.     

Intrinsic thermal stability and quenching recovery of thin-film superconductors with thermal boundary resistance

The stability behaviour of a thin-film superconductor under a localized release of thermal disturbance is investigated. Two-dimensional conjugate film/substrate conduction equation with anisotropic thermal conductivity of the film, and Joule heat are employed to investigate effects of substrate and thermal properties on the intrinsic stability and quenching recovery. To consider the thermal boundary resistance between film and substrate, an interfacial-layer model (ILM) with very low diffusivity and an acoustic mismatch model (AMM) are employed. Results show that the thermal boundary resistance influences strongly the intrinsic stability. Thermal boundary resistance increases intrinsic stability if the thermal conductivity of the substrate or the disturbance energy is large. Higher Biot numbers and thermal conductivity ratios of film to substrate in longitudinal direction influence stability favorably. We demonstrate also that operation of a film/substrate system, such as YBCO/MgO, is either intrinsically stable or irrecoverably unstable.The authors wish to express their sincere appreciation to Dr. R. C. Chen for his invaluable advice and suggestions during the course of this paper. This research was supported by the National Science Council of the R. O. C. through grant NSC 83-0401-E-009-006. The computations were performed on the IBM ES/9000 at the National Center For High-Performance Computing.     

Viscosity solution theory of a class of nonlinear degenerate parabolic equations II. Lipschitz continuity of free boundary

In [1] we construct a unique bounded Hölder continuous viscosity solution for the nonlinear PDEs with the evolutionp-Laplacian equation and its anisotropic version as typical examples. In this part, we investigate the Lipschitz continuity of the free boundary of viscosity solution and its asymptotic spherical symmetricity, however, this result does not include the anisotropic case.This research is supported by the National Natural Sciences Foundation of China.     

Bager第五图的完善

１９８９年发表的Ｂａｇｅｒ第五图，包含关于三角形元素的３５个二次规范画数之间的５１个不等式通过细致的分析，本文给出了其中遗漏的１２个基本不等式