THE GLOBAL EXISTENCE OF STRONG SOLUTIONS TO THERMOMECHANICAL CUCKER-SMALE-STOKES EQUATIONS IN THE WHOLE DOMAIN

We study the global existence and uniqueness of a strong solution to the kinetic thermomechanical Cucker-Smale(for short,TCS) model coupled with Stokes equations in the whole space.The coupled system consists of the kinetic TCS equation for a particle ensemble and the Stokes equations for a fluid via a drag force.In this paper,we present a complete analysis of the existence of global-in-time strong solutions to the coupled model without any smallness restrictions on the initial data.

Existence of Solutions of a Convolution Integral Equation

In this study, we prove the of existence of solutions of a convolution Volterra integral equation in the space of the Lebesgue integrable function on the set of positive real numbers and with the standard norm defined on it. An operator P was assigned to the convolution integral operator which was later expressed in terms of the superposition operator and the nonlinear operator. Given a ball Br belonging to the space L it was established that the operator P maps the ball into itself. The Hausdorff measure of noncompactness was then applied by first proving that given a set M∈ B r the set is bounded, closed, convex and nondecreasing. Finally, the Darbo fixed point theorem was applied on the measure obtained from the set E belonging to M. From this application, it was observed that the conditions for the Darbo fixed point theorem was satisfied. This indicated the presence of at least a fixed point for the integral equation which thereby implying the existence of solutions for the integral equation.

Global Existence and Decay of Solutions for a Class of a Pseudo-Parabolic Equation with Singular Potential and Logarithmic Nonlocal Source

This article investigates the well posedness and asymptotic behavior of Neumann initial boundary value problems for a class of pseudo-parabolic equations with singular potential and logarithmic nonlinearity. By utilizing cut-off techniques and combining with the Faedo Galerkin approximation method, local solvability was established. Based on the potential well method and Hardy Sobolev inequality, derive the global existence of the solution. In addition, we also obtained the results of decay.

Existence of Monotone Positive Solution for a Fourth-Order Three-Point BVP with Sign-Changing Green’s Function

This paper is concerned with the following fourth-order three-point boundary value problem , where , we discuss the existence of positive solutions to the above problem by applying to the fixed point theory in cones and iterative technique.

Global Existence of the Solution for a Reduced Model of the Vectorial Quantum Zakharov System

In this paper, we study the global existence of the smooth solution for a reduced quantum Zakharov system in two spatial dimensions. Using energy estimates and the logarithmic type Sobolev inequality, we show the global existence of the solution to this system without any small condition on the initial data.

THE EXISTENCE AND MULTIPLICITY OF k-CONVEX SOLUTIONS FOR A COUPLED k-HESSIAN SYSTEM

In this paper,we focus on the following coupled system of k-Hessian equations:{S_(k)(λ(D^(2)u))=f_(1)(|x|,-v)in B,S_(k)(λ(D^(2)v))=f2(|x|,-u)in B,u=v=0 on■B.Here B is a unit ball with center 0 and fi(i=1,2)are continuous and nonnegative functions.By introducing some new growth conditions on the nonlinearities f_(1) and f_(2),which are more flexible than the existing conditions for the k-Hessian systems(equations),several new existence and multiplicity results for k-convex solutions for this kind of problem are obtained.

SUFFICIENT AND NECESSARY CONDITIONS ON THE EXISTENCE AND ESTIMATES OF BOUNDARY BLOW-UP SOLUTIONS FOR SINGULAR p-LAPLACIAN EQUATIONS

Let?denote a smooth,bounded domain in R^(N)(N≥2).Suppose that g is a nondecreasing C^(1)positive function and assume that b(x)is continuous and nonnegative inΩ,and that it may be singular on■Ω.In this paper,we provide sufficient and necessary conditions on the existence of boundary blow-up solutions to the p-Laplacian problem△_(p)u=b(x)g(u)for x∈Ω,u(x)→+∞as dist(x,■Ω)→0.The estimates of such solutions are also investigated.Moreover,when b has strong singularity,the nonexistence of boundary blow-up(radial)solutions and infinitely many radial solutions are also considered.

THE EXISTENCE OF GLOBAL SOLUTIONS FOR THE FULL NAVIER-STOKES-KORTEWEG SYSTEM OF VAN DER WAALS GAS

The aim of this work is to prove the existence for the global solution of a nonisothermal or non-isentropic model of capillary compressible fluids derived by J.E.Dunn and J.Serrin(1985),in the case of van der Waals gas.Under the small initial perturbation,the proof of the global existence is based on an elementary energy method using the continuation argument of local solution.Moreover,the uniqueness of global solutions and large time behavior of the density are given.It is one of the main difficulties that the pressure p is not the increasing function of the densityρ.

Effect of existence state of asphaltenes on the asphaltenes-wax interaction in wax deposition

Asphaltenes are the most elusive substances in waxy crude oil,especially the complex structures,which leads to significant precipitation and aggregation characteristics of asphaltenes,and affects the asphaltenes-wax interaction.In this study,the concept of the existence state of asphaltenes was introduced to semi-quantitatively investigate the precipitation and aggregation characteristics of asphaltenes.On this basis,the influence of the existence state of asphaltenes on wax deposition was studied by coldfinger device and high-temperature gas chromatography,and the composition and properties of the deposits were analyzed.Four main findings were made:(1)As the asphaltene concentration increases,the existence state of asphaltenes gradually transitions from dispersed state to aggregated state,and the asphaltene concentration of 0.30 wt%in this study is the starting point of the transition.(2)The existence state of asphaltenes in crude oil does affect the process of wax deposition,as shown in the fact that the dispersed asphaltenes promote the occurrence of wax deposition,while the aggregated asphaltenes can inhibit wax deposition.(3)In the presence of the aggregated asphaltenes,that is,when the asphaltene concentration is higher than 0.30 wt%,the shedding phenomenon of deposit layer was observed,and with the increase of aggregated asphaltenes,the deposit layer fell off earlier.(4)With the increase of the dispersed asphaltenes,the wax appearance temperature(WAT)and wax content of the deposits all showed an increasing trend,while with the appearance of the aggregated asphaltenes,the above situation was reversed.The findings of this study can help for better understanding of the interaction between the asphaltenes and wax in wax deposition.

The existence of radial k-admissible solutions for n-dimension system of k-Hessian equations

In this paper,we focus on a general n-dimension system of k-Hessian equations.By introducing some new suitable growth conditions,the existence results of radial k-admissible solutions of the k-Hessian system are obtained.Our approach is largely based on the well-known fixed-point theorem.

THE EXISTENCE AND LOCAL UNIQUENESS OF MULTI-PEAK SOLUTIONS TO A CLASS OF KIRCHHOFF TYPE EQUATIONS

In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate critical points of the potential function V(x),where a,b>0,1<p<5 are constants,andε>0 is a parameter.Applying the Lyapunov-Schmidt reduction method and a local Pohozaev type identity,we establish the existence and local uniqueness results of multi-peak solutions,which concentrate at{a_(i)}1≤i≤k,where{a_(i)}1≤i≤k are non-degenerate critical points of V(x)asε→0.

THE EXISTENCE OF WEAK SOLUTIONS AND PROPAGATION REGULARITY FOR A GENERALIZED KDV SYSTEM

This paper examines the existence of weak solutions to a class of the high-order Korteweg-de Vries(KdV)system in Rn.We first prove,by the Leray-Schauder principle and the vanishing viscosity method,that any initial data N-dimensional vector value function u0(x)in Sobolev space H^(s)(R^(n))(s≥1)leads to a global weak solution.Second,we investigate some special regularity properties of solutions to the initial value problem associated with the KdV type system in R^(2)and R^(3).

Construction of Legal System of China's Farmland Protection under the Coexistence of Multiple Objectives:Historical Logic,Practical Problems and Optimization Paths

[Objectives]To explore the evolution of the legal system of farmland protection and explore the rules and characteristics of policy development based on the theory and logic of institutional change since China's reform and opening up,reveal the problems and deep-seated reasons of its legislation,clarify the direction of farmland protection in the new period,and solve the"non-agricultural""non-grain"and ecological problems of farmland.[Methods]Literature analysis and inductive deduction methods were used.[Results]The evolution of the farmland protection legal system has gone through the process of"national consciousness-policy guidelines-institutional system",the change from"single subject to multiple subjects";change from the use of"one-way administrative means to coordinated use of administrative,economic and technical means".The practical problems of the farmland protection legal system are mainly due to the insufficient systematization of the farmland protection legal system itself,the generalization of quantity protection,the transformation of quality protection,and the absence of ecological protection.[Conclusions]It is recommended to improve the existing farmland protection legal system from the establishment of the Farmland Protection Law,the improvement of the farmland protection public participation mechanism and supervision mechanism,the establishment of the farmland quality construction and improvement system,the differentiated farmland occupation and supplementation balance system,and the ecological restoration system.

Existence and Uniqueness Results for a Fully Third-Order Boundary Value Problem

The boundary value problems of the third-order ordinary differential equation have many practical application backgrounds and their some special cases have been studied by many authors. However, few scholars have studied the boundary value problems of the complete third-order differential equations u′′′(t) = f (t,u(t),u′(t),u′′(t)). In this paper, we discuss the existence and uniqueness of solutions and positive solutions of the fully third-order ordinary differential equation on [0,1] with the boundary condition u(0) = u′(1) = u′′(1) = 0. Under some inequality conditions on nonlinearity f some new existence and uniqueness results of solutions and positive solutions are obtained.

Existence and Stability of Solutions for a Class of Fractional Impulsive Differential Equations with Atangana-Baleanu-Caputo Derivative

In this paper, we are concerned with the existence of solutions to a class of Atangana-Baleanu-Caputo impulsive fractional differential equation. The existence and uniqueness of the solution of the fractional differential equation are obtained by Banach and Krasnoselakii fixed point theorems, and sufficient conditions for the existence and uniqueness of the solution are also developed. In addition, the Hyers-Ulam stability of the solution is considered. At last, an example is given to illustrate the main results.

The Three Aspects of “Human Existence” from the Human Rights Perspective

At present,the West overrides the east in international human rights discourse.In order to break through the shackles,it is imperative to provide legal support for China’s human rights discourse.taking the concept of“human existence”as the fulcrum and comparing it with nature,otherness,and community as the reference,the human being showcases triple facets:“individual person”,“person in relations”,and“person with rights”,which correspond to the three personal perspectives and progressively deduce the subjectivity of human beings,the world history of human rights,and the comprehensive and free development of human rights discourse.the concept of“individual person”is the starting point of human rights,and the harmonious,moral concept of subjectivity provides an orderly basis for the importance of the“right to subsistence and right to development”.“person in relations”represents the externality of human rights,and the world-historical view of time and space has laid the value foundation for the unity of“universality and particularity of human rights”.“person with rights”is the goal of human rights,and the concept of cooperation for the well-rounded and free development of human rights paves the conceptual way for the realization of people’s well-being.

Unity is the Vital Cornerstone of Human Existence

Any journalist would consider it a career highlight to cover a major historical event or witness a ground-breaking breakthrough.I am thankful that the milestone 20th National Congress of the Communist Party of China (CPC) came as a fortuitous stroke of serendipity in my professional life.

化工职教师范生培养存在的问题与对策

近几年国家大力发展化工职业教育,取得了一定成果。化工职教师范生是我国化工职教师资的重要来源。培养既具有师范教育能力,又具有职业教育能力,还具有优良职业德行的化工职教师范生是发展高质量现代化工职业教育的需要。文中阐述了目前化工职教师范培养中存在的若干问题,并针对问题提出相应的对策,以期提高化工职教师范生培养的质量。

基于变形影响的基坑邻近建筑保护措施研究

城市土地资源的紧张促进了城市地下空间的开发,同时,大量的基坑工程紧邻既有建构筑物,为工程建设带来极大的挑战。随着深基坑的设计理念由“强度控制”转变为“变形控制”,周围既有建筑的保护成为基坑工程中的重点问题。为确保深基坑邻近建筑的安全,综合大量文献资料,总结了深基坑施工引起的建筑变形特征、来源、影响因素和预测方法,基于建筑变形影响因素对目前建筑保护的主要措施和手段进行了分析整理,探讨了各项措施的适应性,结合基坑工程的勘察、建筑保护方案设计、基坑工程施工和信息化施工监测提出了基坑邻近建筑保护综合体系,以期为相关工程和研究提供参考与建议。

儒家传统“即身德育”思想及其教化路径

异于西方绵延千年的身心二元论思想,中国儒家传统伦理思想坚持灵肉圆融,并由此演化生成了独具特色的“即身德育”范式。首先,即身德育不仅强调德育必须兼顾身心发展,而且将身体拓宽到与个体、时空、世界交汇的伦理情境;其次,随着“藏礼于器”将“礼”生活化,个体得以始终浸身于器物无言之教的陶冶中,从而在潜移默化间顺应了道德要求;最后,依托于实践和体悟将外在的伦理规范内化为即身的道德智慧后,个体便能在应然的道德律法中觅得道德选择的自由,从而在生活中实现德性生存。研究儒家传统即身德育思想及其教化路径,既可为当代德育提供镜鉴,亦可为建构中国自主德育知识体系探寻丰富的思想资源。