THE GLOBAL EXISTENCE AND UNIQUENESS OF SMOOTH SOLUTIONS TO A FLUID-PARTICLE INTERACTION MODEL IN THE FLOWING REGIME

This paper is concerned with the Cauchy problem for a 3D fluid-particle interaction model in the so-called flowing regime inℝ3.Under the smallness assumption on both the external potential and the initial perturbation of the stationary solution in some Sobolev spaces,the existence and uniqueness of global smooth solutions in H3 of the system are established by using the careful energy method.

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.

Effect of burial depth of a new tunnel on the seismic response of an existing tunnel

Burial depth is a crucial factor affecting the forces and deformation of tunnels during earthquakes.One key issue is a lack of understanding of the effect of a change in the buried depth of a single-side tunnel on the seismic response of a double-tunnel system.In this study,shaking table tests were designed and performed based on a tunnel under construction in Dalian,China.Numerical models were established using the equivalent linear method combined with ABAQUS finite element software to analyze the seismic response of the interacting system.The results showed that the amplification coefficient of the soil acceleration did not change evidently with the burial depth of the new tunnel but decreased as the seismic amplitude increased.In addition,the existing tunnel acceleration,earth pressure,and internal force were hardly affected by the change in the burial depth;for the new tunnel,the acceleration and internal force decreased as the burial depth increased,while the earth pressure increased.This shows that the earth pressure distribution in a double-tunnel system is relatively complex and mainly concentrated on the arch spandrel and arch springing of the relative area.Overall,when the horizontal clearance between the center of the two tunnels was more than twice the sum of the radius of the outer edges of the two tunnels,the change in the burial depth of the new tunnel had little effect on the existing one,and the tunnel structure was deemed safe.These results provide a preliminary understanding and reference for the seismic performance of a double-tunnel system.

The Existence of Solutions for Kirchhoff-Type Equations with General Singular Terms

We study the existence of solutions for Kirchhoff-type equations.Firstly,we use the Sobolev inequality and the weakly lower semi-continuity of the norm to prove that the corresponding function can reach the global minimum.Then,we use the variational method and some analytical techniques to obtain the existence of the positive solution of the equation whenλis small enough.

Durability evaluation for existing railway engineering: a review

Purpose – This study aims to analyze the factors, evaluation techniques of the durability of existing railwayengineering.Design/methodology/approach – China has built a railway network of over 150,000 km. Ensuring thesafety of the existing railway engineering is of great significance for maintaining normal railway operationorder. However, railway engineering is a strip structure that crosses multiple complex environments. Andrailway engineering will withstand high-frequency impact loads from trains. The above factors have led todifferences in the deterioration characteristics and maintenance strategies of railway engineering compared toconventional concrete structures. Therefore, it is very important to analyze the key factors that affect thedurability of railway structures and propose technologies for durability evaluation.Findings – The factors that affect the durability and reliability of railway engineering are mainly divided intothree categories: material factors, environmental factors and load factors. Among them, material factors alsoinclude influencing factors, such as raw materials, mix proportions and so on. Environmental factors varydepending on the service environment of railway engineering, and the durability and deterioration of concretehave different failure mechanisms. Load factors include static load and train dynamic load. The on-site rapiddetection methods for five common diseases in railway engineering are also proposed in this paper. Thesemethods can quickly evaluate the durability of existing railway engineering concrete.Originality/value – The research can provide some new evaluation techniques and methods for thedurability of existing railway engineering.

Existence of Entropy Solution for Degenerate Parabolic-Hyperbolic Problem Involving p(x)-Laplacian with Neumann Boundary Condition

We consider a strongly non-linear degenerate parabolic-hyperbolic problem with p(x)-Laplacian diffusion flux function. We propose an entropy formulation and prove the existence of an entropy solution.

A Preliminary Discussion on Watercolor Creation and Emotional Expression of Female Themes in the 20th Century

The history of watercolor painting spans over three centuries,and the study of watercolor creations focusing on female themes have been a hot topic in the subfield of art studies.Watercolor originated in the Age of Exploration,initially serving as a practical tool for natural history,and later evolving into an art form for the aristocracy.In the 20th century,creations featuring female themes flourished and reached their peak.Compared to early works portraying female theses in mythology and religion,these paintings exhibit significant differences in expression,color,and texture,reflecting the gradual rise of women’s status and the artists’reflections on modern society.This article delves into the development,emotional expression,creation,and inspiration of watercolor paintings with female themes.By analyzing representative works,we explore the artists’portrayal of women and the reflection of women’s living conditions,social status,and ideological consciousness in contemporary society.This article also examines the profound influence and artistic value of these works on contemporary female-themed paintings from the perspective of art studies.

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.

Operation optimization strategy of existing residential building energy-saving renovation market:From the perspective of subject behavior

The energy-saving renovation of existing residential buildings is a crucial measure to achieve the strategic goal of energy conservation and emission reduction in China and build ecologically livable cities.This article focuses on the perspective of subject behavior,starting from analyzing the current situation and difficulties of the operation of the energy-saving renovation market for existing residential buildings in China,drawing on the practical experience of the operation of the existing residential building energy-saving renovation market abroad.Based on principles such as systematicity,humanization,feasibility,and sustainability,the article constructs an operation optimization system of the existing residential building energy-saving renovation market from the perspective of subject behavior.In order to provide a reference for the healthy and orderly operation of the existing residential building energy-saving renovation market,this paper proposes implementation strategies for optimizing the operation of the existing residential building energy-saving renovation market.Suggestions are proposed from four aspects:optimizing the market environment,innovating the financing model,building the information sharing platform,and utilizing the synergies of the main subjects.

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.

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.

Application of Chinese Ethnic Minority Themes in Contemporary Figurative Sculpture Creation

In the field of contemporary sculpture creation,the rich culture and historical depth of Chinese ethnic minorities have attracted the widespread attention of artists.These creations not only emphasize external features such as ethnic costumes,totems,or life scenes but also touch deep spiritual contents including historical stories,religious beliefs,and living habits of ethnic minorities.This paper discusses the integration process of Chinese ethnic minority themes in figurative sculpture creation and the inheritance of the profound spirit of ethnic groups in this process.At the same time,this paper also places the diversified expression and innovative practice of these themes in sculpture art in the context of the new era for investigation and explores the far-reaching influence of its development on promoting cultural inheritance and artistic innovation.

On the Theme of Coexistence of Opposites in The Left Hand of Darkness

As one of the best-known literary works of the American novelist Ursula K.Le Guin,The Left Hand of Darkness is not only successful in its splendid plots and beautiful language but also in the important function of its readers in reading.In the thesis,one of its themes,coexistence of opposites,is analyzed in the reader response perspective in order to reveal Le Guin's reader-consciousness.The theme exists on a higher level in the novel and expresses Le Guin's attitude towards life and universe.Le Guin unified her own philosophy in the novel and tried to call for the reader's resonance.

Existentialist Articulation in the Themes of The Enigma

The main line of John Fowles' short story The Enigma is the missing of John Marcus Fielding. It mainly narrates people's views on Mr. Fielding, attitudes to him and attempts to clear the mystery up. Fowles inherits the concept of postmodernism in terms of themes, narration and other aspects, which gives a further and deeper expression of his views on freedom, mystery and the relationship between author, characters and readers. In particular, this short story of John Fowles, who was influenced by existentialism, carries out a profound literary interpretation of existentialism in many aspects. Focusing on the themes, the paper will look at the existentialist articulation in The Enigma.

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).

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.

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.

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 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.