MULTIPLE POSITIVE SOLUTIONS FOR A CLASS OF QUASI-LINEAR ELLIPTIC EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENT

In this paper, we study the multiplicity results of positive solutions for a class of quasi-linear elliptic equations involving critical Sobolev exponent. With the help of Nehari manifold and a mini-max principle, we prove that problem admits at least two or three positive solutions under different conditions.

Simulation of Quasi-Linear Mesoscale Convective Systems in Northern China：Lightning Activities and Storm Structure

Two intense quasi-linear mesoscale convective systems（QLMCSs） in northern China were simulated using the WRF（Weather Research and Forecasting） model and the 3D-Var（three-dimensional variational） analysis system of the ARPS（Advanced Regional Prediction System） model.A new method in which the lightning density is calculated using both the precipitation and non-precipitation ice mass was developed to reveal the relationship between the lightning activities and QLMCS structures.Results indicate that,compared with calculating the results using two previous methods,the lightning density calculated using the new method presented in this study is in better accordance with observations.Based on the calculated lightning densities using the new method,it was found that most lightning activity was initiated on the right side and at the front of the QLMCSs,where the surface wind field converged intensely.The CAPE was much stronger ahead of the southeastward progressing QLMCS than to the back it,and their lightning events mainly occurred in regions with a large gradient of CAPE.Comparisons between lightning and non-lightning regions indicated that lightning regions featured more intense ascending motion than non-lightning regions;the vertical ranges of maximum reflectivity between lightning and non-lightning regions were very different;and the ice mixing ratio featured no significant differences between the lightning and non-lightning regions.

A PRIORI ESTIMATE FOR MAXIMUM MODULUS OF GENERALIZED SOLUTIONS OF QUASI-LINEAR ELLIPTIC EQUATIONS

Let G he a hounded domain in E Consider the following quasi-linear elliptic equationAlthough the houndedness of generalized solutions of the equation is proved for very general structural conditions, it does not supply a priori estimate for maximum modulus of solutions. In this paper an estimate to the maximum modulus is made firstly for a special case of quasi-linear elliptic equations, i.e. the A and B satisfy the following structural conditions

THE ESTIMATION OF SOLUTION OF THE BOUNDARY VALUE PROBLEM OF THE SYSTEMS FOR QUASI-LINEAR ORDINARY DIFFERENTIAL EQUATIONS

This paper deals with the singular perturbation of the boundary value problem of the systems for quasi-linear ordinary differential equationswhere x,f, y , h, A, B and C all belong to Rn , and g is an n×n matrix function. Under suitable conditions we prove the existence of the solutions by diagonalization and the fixed point theorem and also estimate the remainder.

EXISTENCE OF POSITIVE SOLUTIONS TO QUASI-LINEAR EQUATION INVOLVING CRITICAL SOBOLEV-HARDY EXPONENT

This paper is concerned with the quasi-linear equation with critical Sobolev-Hardy exponentwhere Ω(?) RN(N(?)3) is a smooth bounded domain, 0∈Ω,0(?)s<p, 1<p< N,p(s) := p(N-s)/N-p is the critical Sobolev-Hardy exponent, λ>0,p(?)r < p ,p := Np/N-p is the critical Sobolev exponent, μ>, 0(?)t < p,p (?) q < p (t) =p(N-t)/N-p. The existence of a positive solution is proved by Sobolev-Hardy inequality and variational method.

Entropy generation analysis of tangent hyperbolic fluid in quadratic Boussinesq approximation using spectral quasi-linearization method

In many industrial applications,heat transfer and tangent hyperbolic fluid flow processes have been garnering increasing attention,owing to their immense importance in technology,engineering,and science.These processes are relevant for polymer solutions,porous industrial materials,ceramic processing,oil recovery,and fluid beds.The present tangent hyperbolic fluid flow and heat transfer model accurately predicts the shear-thinning phenomenon and describes the blood flow characteristics.Therefore,the entropy production analysis of a non-Newtonian tangent hyperbolic material flow through a vertical microchannel with a quadratic density temperature fluctuation(quadratic/nonlinear Boussinesq approximation)is performed in the present study.The impacts of the hydrodynamic flow and Newton’s thermal conditions on the flow,heat transfer,and entropy generation are analyzed.The governing nonlinear equations are solved with the spectral quasi-linearization method(SQLM).The obtained results are compared with those calculated with a finite element method and the bvp4c routine.In addition,the effects of key parameters on the velocity of the hyperbolic tangent material,the entropy generation,the temperature,and the Nusselt number are discussed.The entropy generation increases with the buoyancy force,the pressure gradient factor,the non-linear convection,and the Eckert number.The non-Newtonian fluid factor improves the magnitude of the velocity field.The power-law index of the hyperbolic fluid and the Weissenberg number are found to be favorable for increasing the temperature field.The buoyancy force caused by the nonlinear change in the fluid density versus temperature improves the thermal energy of the system.

THE INITIAL BOUNDARY VALUE PROBLEM FOR QUASI-LINEAR SCHRODINGER-POISSON EQUATIONS

In this article, the author studies the iuitial （Dirichlet.） boundary problem for a high field version of the Schroedinger-Poisson equations, which include a nonlinear term in the Poisson equation corresponding to a field-dependent dielectric constant and an effective potential in the Schroedinger equations on the unit cube. h global existence and uniqueness is established for a solution to this problem.

Approximate derivative-dependent functional variable separation for quasi-linear diffusion equations with a weak source

By using the approximate derivative-dependent functional variable separation approach, we study the quasi-linear diffusion equations with a weak source ut = （A（u）Ux）x ＋ eB（u, Ux）. A complete classification of these perturbed equations which admit approximate derivative-dependent functional separable solutions is listed. As a consequence, some approxi- mate solutions to the resulting perturbed equations are constructed via examples.

An O(k²+kh²+h²) Accurate Two-level Implicit Cubic Spline Method for One Space Dimensional Quasi-linear Parabolic Equations

In this piece of work, using three spatial grid points, we discuss a new two-level implicit cubic spline method of O(k2 + kh2 + h4) for the solution of quasi-linear parabolic equation , 0 0 subject to appropriate initial and Dirichlet boundary conditions, where h > 0, k > 0 are grid sizes in space and time-directions, respectively. The cubic spline approximation produces at each time level a spline function which may be used to obtain the solution at any point in the range of the space variable. The proposed cubic spline method is applicable to parabolic equations having singularity. The stability analysis for diffusion- convection equation shows the unconditionally stable character of the cubic spline method. The numerical tests are performed and comparative results are provided to illustrate the usefulness of the proposed method.

Symmetry Reductions of Cauchy Problems for Fourth-Order Quasi-Linear Parabolic Equations

这份报纸被奉献给为承认某些概括有条件的对称(GCS ) 的第四顺序的伪线性的寓言的方程学习 Cauchy 问题的对称减小。完全的组分类结果被介绍，并且一些例子被给显示出主要减小过程。

A Class of Quasi-Linear Riemann-Hilbert Problems for General Holomorphic Functions in the Unit Disk

In this paper, a class of quasi linear Riemann Hilbert problems for general holomorphic functions in the unit disk was studied. Under suitable hypotheses, the existence of solutions of the Hardy class H 2 to this problem was proved by means of Tikhonov's fixed point theorem and corresponding theories for general holomorphic functions.

Solutions and Conditional Lie-Backlund Symmetries of Quasi-linear Diffusion-Reaction Equations

伪线性的散开反应方程的准确解决方案的新类被寻找考虑方程的高顺序的有条件的 Lie-B&#228;cklund 对称获得。这里使用的方法扩大变量和不变的潜水艇空间的导出依赖者的功能的分离的途径。行为到象发作那样的一些答案并且熄灭也被描述。

Global Smooth Solution for the Quasi-linear Wave Equation

在这份报纸，我们为下列伪线性的波浪方程 utt-2kuxxt=(unx ) 学习 Cauchy 问题 x k0 并且是 2 是的实数，和 n 一个整数。我们证明为任何 T0， Cauchy 问题承认唯一的全球光滑的答案 u C ((0， T ] ；H (R)) C ([0， T ] ；H2 (R)) C1 ([0， T ] ；L2 (R)) 在起始的数据上的合适的假设下面。

A Robin Problem for Quasi-linear System

In this paper, a Robin problem for quasi-linear system is considered. Under the appropriate assumptions, the existence of solution for the problem is proved and the asymptotic behavior of the solution is studied using the theory of differential inequalities.

Boundary Value Problems of Quasi-linear Ordinary Differential Equations on the Semi-infinite Interval

积极答案的存在为边界值问题被建立为一个类非退化半无限的间隔上的伪线性的平常的微分方程。结果被使用 Leray-Schauder 方法的非线性的选择获得。

Analysis of Singularity for Reducible Quasi-linear Hyperbolic Systems

In this paper we investigate the formation of singularities of hyperbolic systems.Employing the method of parametric coordinates and the existence of the solution of the blow-up system, we prove that the blow-up of classic solutions is due to the envelope of characteristics of the same family, analyze the geometric properties of the envelope of characteristics and estimate the blowup rates of the solution precisely.

Uniqueness of solution of a quasi-linear Reaction-diffusion system

In this paper,we consider nonnegative classical solutions of a Quasi-linear reaction-diffusion system with nonlinear boundary conditions.We prove the uniqueness of a nonnegative classical solution to this problem.

Infinitely Many Solutions for a Class of Quasi-linear Elliptic Problem

In this paper,we study the following quasi-linear elliptic equation:■where Ω?R^(N) is a bounded domain,λ>0 is a parameter.The function ψ(|t|)t is the subcritical term,and φ(|t|)t is the critical Orlicz-Sobolev growth term with respect to φ.Under appropriate conditions on φ,ψ and φ,we prove the existence of infinitely many weak solutions for quasi-linear elliptic equation,for λ∈(0,λ_(0)),where λ_(0)> 0 is a fixed constant.

基于准线性近似方法的SAR图像海浪参数反演研究

本文根据相干斑噪声的时间快变特征和非海浪纹理现象的时间缓变特征,基于交叉谱提出了一种对相干斑噪声和大尺度非海浪纹理的抑制的方法,进而结合SAR图像谱和海浪谱之间的准线性映射关系,基于SAR数据对海浪参数进行了反演。在反演过程中,首先仿真分析了不同海况下准线性近似法的海浪反演能力,结果表明:风浪引起的方位向截断效应会显著影响反演精度,因此该方法在低风速时的涌浪反演精度更高。通过将基于Sentinel-1卫星2020年的波模式SAR数据的反演结果与欧洲中期天气预报中心(European Centre for Medium-Range Weather Forecasts,ECMWF)提供的再分析数据进行对比,发现高海况海浪有效波高反演结果明显偏低,而且该反演误差与风速、方位向截断波长之间存在显著相关性。为了提高有效波高的反演精度,本文进一步给出了海浪有效波高反演误差与风速、方位向截断波长之间的经验校正函数模型,结果显示,通过该模型修正后的海浪有效波高反演结果与ECMWF数据和浮标测量数据具有良好一致性。

断点回归方法及应用实现

目的完整、系统介绍断点回归设计(RDD)原理及统计方法,为其在公共卫生领域应用提供参考。方法在介绍断点回归设计原理基础上,用室内甲醛干预的实例演示了利用Stata软件实现断点回归统计方法的过程,介绍和比较属于参数法的多项式回归和属于非参数法的局部线性回归的分析方法和结果。结果RDD是一种准实验设计,对研究对象没有随机分组,而是选择一个与干预措施有关的变量,根据该变量的取值选择切点划分干预组和对照组。RDD在内部有效性方面优于其他准实验设计,但外部有效性受到一定限制。基于观察性资料的RDD不仅可控制可观测的混杂因素,还可控制无法观测的混杂因素,也更符合伦理道德。在本文实例中,多项式回归和局部线性回归两种分析方法的结果基本一致。结论RDD在公共卫生领域的真实世界研究中有广阔的应用前景,为科学评估干预政策和提供高质量决策依据提供新的思路和方法。