EXISTENCE TIME OF SOLUTION OF THE (1+2)D KNOBLOCH EQUATION WITH INITIAL-BOUNDARY VALUE PROBLEM

The equation of pattern formation induced by buoyancy or by surface-tension gradient in finite systems confined between horizontal poor heat conductors is introduced by Knobloch[1990] where u is the planform function, μ is the scaled Rayleigh number, K = 1 and α represents the effects of a heat transfer finite Blot number. The cofficients β, δ and γ do not vanish when the boundary, conditions at top and bottom are not identical (β / 0, δ / 0) or nonBoussinesq effects are taked into account (γ / 0). In this paper, the Knobloch equation with α > 0 is considered, the global existence in L2-space and the finite existence time of solution in V2-space have been obtained respectively.

Initial-boundary value problem of nonlinear hyperbolic system for conservation laws with delta-shock waves

For a nonlinear hyperbolic system of conservation laws, the initial-boundary value problem is concerned with the boundary conditions. A boundary entropy condition is derived based on Dubois F and Le Floch P＇s results by taking a suitable entropy-flux pair （Journal of Differential Equations, 1988, 71（1）： 93-122）. The solutions of the initial-boundary value problem for the system are constructively obtained, in which initial-boundary data are in piecewise constant states. The delta-shock waves appear in their solutions.

GLOBAL EXISTENCE OF WEAKLY DISCONTINUOUS SOLUTIONS TO A KIND OF MIXED INITIAL-BOUNDARY VALUE PROBLEM FOR QUASILINEAR HYPERBOLIC SYSTEMS

In this paper, the mixed initial-boundary value problem for general first order quasi- linear hyperbolic systems with nonlinear boundary conditions in the domain D = {（t, x） ｜ t ≥ 0, x ≥0} is considered. A sufficient condition to guarantee the existence and uniqueness of global weakly discontinuous solution is given.

EXISTENCE AND NONEXISTENCE OF GLOBAL SOLUTIONS OF THE INITIAL-BOUNDARY VALUE PROBLEM FOR SOME DEGENERATE HYPERBOLIC EQUATION

The author considers the global existence and global nonexistence of the initial-boundary value problem for some degenerate hyperbolic equation of the form utt- div（｜△↓｜^P-2 △↓u）=｜u｜^m u, （x,t）∈[0, ＋∞） ×Ω with p 〉 2 and m 〉 0. He deals with the global solutions by D.H.Sattinger＇s potential well ideas. At the same time, when the initial energy is positive, but appropriately bounded, the global nonexistence of solutions is verified by using the analysis method.

THE SECOND INITIAL-BOUNDARY VALUE PROBLEM FOR A QUASILINEAR PARABOLIC EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS

With prior estimate method, the existence, uniqueness, stability and large time behavior of the solution of second initial-boundary value problem for a fast diffusion equation with nonlinear boundary conditions are investigated. The main results are : 1) there exists only one global weak solution which continuously depends on initial value; 2) when t < T-0, the solution is infinitely continuously differentiable and is a classical solution; 3) the solution converges to zero uniformly as t is large enough.

Initial-boundary value problem of one class of nonlinear Schrdinger equations described in molecular crystals

In this paper, we study the initiial-boundary value problem of one class of nonlinear Schrodinger equations described in molecular crystals. Furthermore, the existence of the global solution is obtained by means of interpolation inequality and a priori estimation.

INHOMOGENEOUS INITIAL-BOUNDARY VALUE PROBLEM FOR GINZBURG-LANDAU EQUATIONS

Some integral identities of smooth solution of inhomogeneous initial boundary value problem of Ginzburg-Landau equations were deduced, by which a priori estimates of the square norm on boundary of normal derivative and the square norm of partial derivatives were obtained. Then the existence of global weak solution of inhomogeneous initial-boundary value problem of Ginzburg-Landau equations was proved by the method of approximation technique and a priori estimates and making limit.

Well-posedness of the time-varying linear electromagnetic initial-boundary value proble

The well-posedness of the initial-boundary value problem of the time-varying linear electromagnetic field in a multi-medium region is investigated. Function spaces are defined, with Faraday＇s law of electromagnetic induction and the initial-boundary conditions considered as constraints. Gauss＇s formula applied to a multi-medium region is used to derive the energy-estimating inequality. After converting the initial-boundary conditions into homogeneous ones and analysing the characteristics of an operator introduced according to the total current law, the existence, uniqueness and stability of the weak solution to the initial-boundary value problem of the time-varying linear electromagnetic field are proved.

Godunov＇s method for initial-boundary value problem of scalar conservation laws

This paper is concerned with Godunov＇s scheme for the initial-boundary value problem of scalar conservation laws. A kind of Godunov＇s scheme, which satisfies the boundary entropy condition, was given. By use of the scheme, numerical simulation for the weak entropy solution to the initial-boundary value problem of scalar conservation laws is conducted.

The Third Initial-boundary Value Problem for a Class of Parabolic Monge-Ampère Equations

For the more general parabolic Monge-Ampère equations defined by the operator F （D2u ＋ σ（x））, the existence and uniqueness of the admissible solution to the third initial-boundary value problem for the equation are established. A new structure condition which is used to get a priori estimate is established.

SEVERAL NEW TYPES OF FINITE-DIFFERENCE SCHEMES FOR SHALLOW-WATER EQUATION WITH INITIAL-BOUNDARY VALUE AND THEIR NUMERICAL EXPERIMENT

This paper proposed several new types of finite-difference methods for the shallow water equation in absolute coordinate system and put forward an effective two-step predictor-corrector method, a compact and iterative algorithm for five diagonal matrix. Then the iterative method was used for a multi-grid procedure for shallow water equation. A t last, an initial-boundary value problem was considered, and the numerical results show that the linear sinusoidal wave would successively evolve into conoidal wave.

INITIAL-BOUNDARY VALUE PROBLEM AND CAUCHY PROBLEM FOR A QUASILINEAR EVOLUTION EQUATION

In the present paper,the local existence of classical solutions to the periodic boundary problem and the Cauchy problem of a quasilinear evolution equation are studied under the assumptions that do not require the monotonicity of σi(s) (i= 1,…, n). The nonexistence of global solutions to the initial-boundary value problem of the equation is also discussed, a blowup theorem is proved and a concrete example is given.

Numerical Treatment of Initial-Boundary Value Problems with Mixed Boundary Conditions

In this paper, we extend the reliable modification of the Adomian Decom-position Method coupled to the Lesnic’s approach to solve boundary value problems and initial boundary value problems with mixed boundary conditions for linear and nonlinear partial differential equations. The method is applied to different forms of heat and wave equations as illustrative examples to exhibit the effectiveness of the method. The method provides the solution in a rapidly convergent series with components that can be computed iteratively. The numerical results for the illustrative examples obtained show remarkable agreement with the exact solutions. We also provide some graphical representations for clear-cut comparisons between the solutions using Maple software.

SINGULAR PERTURBATION OF INITIAL-BOUNDARY VALUE PROBLEMS FOR A CLASS OF REACTION DIFFUSION SYSTEMS

In this paper, a class of singularly perturbed initial-boundary value problems for the reaction diffusion systems is considered. Using the theory of differential inequality, we prove that the initial-boundary value problems have a solution and obtain their asymptotic expansion.

Construction of Global Weak Entropy Solution of Initial-Boundary Value Problem for Scalar Conservation Laws with Weak Discontinuous Flux

This paper is concerned with the initial-boundary value problem of scalar conservation laws with weak discontinuous flux, whose initial data are a function with two pieces of constant and whose boundary data are a constant function. Under the condition that the flux function has a finite number of weak discontinuous points, by using the structure of weak entropy solution of the corresponding initial value problem and the boundary entropy condition developed by Bardos-Leroux-Nedelec, we give a construction method to the global weak entropy solution for this initial-boundary value problem, and by investigating the interaction of elementary waves and the boundary, we clarify the geometric structure and the behavior of boundary for the weak entropy solution.

AN EXPONENTIALLY FITTED DIFFERENCE SCHEME FOR THE HYPERBOLIC-HYPERBOLIC SINGULARLY PERTURBED INITIAL-BOUNDARY VALUE PROBLEM

In this paper we discuss, an initial-boundary value problem of hyperbolic type with first derivative with respect to x. The asymptotic solution is constructed and its uniform validity is proved under weader compatibility conditions. Then we develop an exponentially fitted difference scheme and establish discrete energy inequality. Finally, we prove that the solution of difference problem uniformly converges to the solution of the original problem.

基于Valued ERGMs模型的核心技术网络成长机制研究——以量子计算领域为例

对核心技术网络及其成长机制的研究有助于梳理核心技术之间的依赖和促进关系,为研究核心技术演化提供新的理论视角和方法。以技术演化相关理论为基础,归纳核心技术网络成长的影响因素,基于量子计算领域专利数据,识别以技术概念和技术关系为基础的量子计算领域核心技术网络,并基于Valued ERGMs模型构建核心技术网络成长机制模型。结果表明,技术要素中心性、专利技术研发能力、与TRIZ进化法则匹配程度以及技术要素同配性对核心技术网络成长具有正向促进作用;在技术路径方面,核心技术网络成长受到技术要素路径依赖性和技术突破的双重影响。最后,根据量子计算领域核心技术网络成长机制的实证研究结果,从技术研发层面、企业层面、政府层面为相关领域技术发展提出策略建议。

The Economics of Competing Water Uses under a FERC Licensing Agreement: Estimation of Property Value, Recreation, and Hydroelectric Impacts

Reservoirs provide a variety of services with economic values across multiple sectors. As demands for reservoir services continue to grow and precipitation patterns evolve, it becomes ever more important to consider the integrated suite of values and tradeoffs that attend changes in water uses and availability. Section 316 (b) of the Clean Water Act requires that owners of certain water cooled power plants evaluate technologies and operational measures that can reduce their impacts to aquatic organisms. The studies must discuss the social costs and benefits of alternative technologies including cooling towers (79 Fed. Reg. 158, 48300 - 48439). Cooling towers achieve their effect through evaporation. This manuscript estimates the property value, recreation, and hydroelectric generation impacts that could result from the evaporative water loss associated with installing cooling towers at the McGuire Nuclear Generating Station (McGuire) located on Lake Norman, North Carolina. Although this study specifically evaluates the effects of evaporative water loss from cooling towers, its methods are applicable to estimating the economic benefits and costs of a new water user or reduced water input in any complex reservoir system that supports steam electric generation, hydroelectric generation, residential properties, recreation, irrigation, and municipal water use.

Decision Making Based on Valued Fuzzy Superhypergraphs

This paper explores the defects in fuzzy (hyper) graphs (as complex (hyper) networks) and extends the fuzzy(hyper) graphs to fuzzy (quasi) superhypergraphs as a new concept.We have modeled the fuzzy superhypergraphsas complex superhypernetworks in order to make a relation between labeled objects in the form of details andgeneralities. Indeed, the structure of fuzzy (quasi) superhypergraphs collects groups of labeled objects and analyzesthem in the form of the part to part of objects, the part of objects to the whole group of objects, and the whole tothe whole group of objects at the same time.We have investigated the properties of fuzzy (quasi) superhypergraphsbased on any positive real number as valued fuzzy (quasi) superhypergraphs, considering the complement of valuedfuzzy (quasi) superhypergraphs, the notation of isomorphism of valued fuzzy (quasi) superhypergraphs based onthe permutations, and we have presented the isomorphic conditions of (self complemented) valued fuzzy (quasi)superhypergraphs. The concept of impact membership value of fuzzy (quasi) superhypergraphs is introducedin this study and it is applied in designing the real problem in the real world. Finally, the problem of businesssuperhypernetworks is presented as an application of fuzzy valued quasi superhypergraphs in the real world.

Effect of Biostimulants Based on Natural Products on the Growth and Nutritional Value of Bean (Phaseolus vulgaris L.)

Beans (Phaseolus vulgaris L.) are widely grown in Cameroon and play a key role in the fight against food insecurity, malnutrition and poverty. However, its cultivation encounters problems due to abiotic and biotic stresses, which leads to the use of synthetic fertilizers and pesticides, which cause significant damage to the environment and human health due to the presence of synthetics residues in the seeds, pods and in the leaves that are eaten. Promoting the use of natural products is becoming a necessity for organic and eco-responsible agriculture that limits contamination problems and improves people’s purchasing power. This study aims to assess the effect of biostimulants based on natural products on the growth and nutritional value of common bean (Phaseolus vulgaris L.). Bean seedlings from white variety (MEX-142) and red variety (DOR-701) were treated every seven days in the field from their pre-emergence, emergence and growth to their maturation under a randomized block experimental design. Six treatments and three repetitions with the biostimulants based on natural products and controls were thus performed and the agromorphological parameters were measured. After 120 days, the contents of growth biomarkers and defense-related enzymes were evaluated in leaves, while the contents of macromolecules, minerals and antinutrients were evaluated in seeds. These biostimulants significantly increased (P P < 0.0001) of antinutrients including oxalates, phytates, tannins and saponins in seeds compared to controls (T+ and T−). Treatment with biostimulants, in particular BS4, improves the performance of bean plants in the field as well as the biofortification of seeds regardless of the variety.